Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

In 10 min , a car with speed of 60 km/h-1 travels how much distance ?

Answer»

60 KMPH TIME = 10 MIN = 10/60 hours = 1/6 hours  distance = speed * time = 60 * 1/6 = 10 km

2.

Differences between solute,solvent and solution?

Answer» NT is a substance which dissolves a SOLUTE. When a solvent dissolves into a solute, it creates a solution. for example: If i pour SALT into a cup of water. The salt is the solute because it's being dissolved and the water is the solvent because it is doing the dissolving. The saltwater is the solution because that's what the solvent and solute make. if this HELPS u mrk it as bst   note
3.

How is diplacement related to velocity and acceleration

Answer»

y= displacement/timeaccleration =velocity/time

4.

A crane operated by an electric motor has a mass of 500kg.it raises a load of 300 kg vertically at a steady speed 0. 2m/s. Assume resistance to be constants at the 1200N.what is the power required To raise. The load.

Answer»

of the crane + WEIGHT of the load = 500 + 300 = 800 kggravitational FORCE due to the weight = 800 * g =  800 * 10  NEWTONS.     Resistance to lifting action of the crane  like friction etc. = 1,200 N  Total force needed to lift the load with a velocity 0.2 m/s = 8,000 + 1,200 Newtonspower needed to lift the load with a velocity (uniform)      P = F * V  =  9, 200 N * 0.2 m/sec =  1, 840 Watts

5.

What is the difference between distance and displacement?

Answer» E: IT IS A SCALAR QUANTITY.                                                                                  DISPLACEMENT: IT IS A VECTOR QUANTITY.
6.

A double convex lens of focal length 30cm is made of glass.When immersed in a liquid of refractive index 1.5 ,the focal length is found to be 120cm. The critical angle between glass and liquids is

Answer»

+ 30 cmLet the refractive index of glass μ_g Liquid of refractive index  μ_l = 1.5   when in air,  the focal length of the DOUBLE convex lens is GIVEN by : the lens MAKER's formula:  1 / f_air = 1/30 = (μ_g - 1) 2 / R ,      R = radius of curvature of the lens surface     1/30 *= (μ_g - 1) 2 / R     μ_g - 1 =  R / 60      --- (1)when immersed in the liquid :        1/f2  = 1/120 = (μ_g / μ_l  - 1) 2 / R         (μ_g /1.5  - 1) = R /240      -- (2)         μ_g  - 1.5 = R / 160        -- (3)            subtract (2) from (1),             0.5 = R/60 - R /160 = R /96          R = 48 cm           μ_g  = 1 + 48/60 = 1.8  as per  (1)                  μ_g / μ_l = 1.8/1.5 = 1.2            critical angle between glass and the liquid :  Sin⁻¹  1/1.2 = Sin⁻¹ 0.833             = 56.44 deg.

7.

In case of a moving body displacement is less than and equal to the distance . explain why?

Answer»

ement is the SHORTEST distance b/w final and INITIAL point and distance is the ACTUAL path covered by moving body.When a body moves in a straight line then their distance and displacement would be same.If body moves in another trajectory (straight line path) then displacement would be LESS than actual distance for eg a body moves in circle ,after COMPLETING one circle then its actual path covered(distance) would be 2πr and shortest distance b/w initial and final point (displacement) would be zero.

8.

an object going down in inclined plane at the acceleration of 5 m/s . find the velocity 3 s after start .

Answer» HAT ,  u = 0time = 3s acceleration = 5 m/s²v = ?    = u + at     = 0 + 5 * 3     = 15 m/s ( ANSWER )
9.

What mean by average velocity.

Answer»

velocity means the total displacement divided by the total time taken.         this is different from the average speed as velocity is a vector.  when we TAKE average we need to take into account the directions of velocity at different times.     if an object travels for time t1  with a UNIFORM velocity   and for time T2  with a uniform velocity  of     then  the average velocity  is      if a person travels for  1 hour  covering a distance of 10 km in a straightline towards the North and then returns along the same STRAIGHT line after 1 hour,  then        v1 vector is 10kmph  towards North.     v2 vector is  10 km ph towards SOUTH.  average velocity is  0.    Average velocity is the net displacement divided by the time interval.

10.

Give an example of each a unitless quantity with dimension a dimensionless quantity with units

Answer»

on less QUANTITY      =  PLANE angle          units  degrees or  RADIANS.  symbol  °     = SOLID angle              units STERADIANS  symbol   symbol  sr==============unit less quantity  ---  but dimension  exists for that quantity.     I wonder if there is a quantity like that.  If there is a dimension, that means there is a unit and there is a way of measuring that.  That means there is no such quantity without a unit but with a dimension .

11.

Derive dimensions of magnetic induction

Answer»

the formula  for a force acting on a CURRENT carrying conductor.              B = magnetic induction = magnetic field strength. Force =  B I L      IE.,  current = I    length  = L  force = newtons.                           let dimensions of current be [ A ]  M L T⁻² =  B  A  L  B = [ M T⁻² A⁻¹ ] =========================we have the formula for magnetic field strength at a POINT d distance AWAY from a current carrying conductor  as :     B = μ₀ I / (2 π d)        this is found by Ampere's circuital law.        μ₀ =  Newtons/Ampere²      B = M L T⁻²  A⁻²   * A  L⁻¹ dimensions      = M T⁻² A⁻¹ units         =  Tesla  or  kg / sec²-Amp        or  Newtons/Amp-meter

12.

The equations of a stationary wave is given by y(x,t)=2sin3.14xcos100*3.14t ,where x and y are measured in meter and t in seconds. Calculate the amplitude, wavelength And frequency of component waves whose superpositions generated this stationary wave.also write the equations of components waves.

Answer»

t ) =  2  Sin 3.14 x    Cos  100 * 3.14 t       x and y are in meters  and t is in seconds.we use the formula in trigonometry  2 Sin A Cos B = Sin (A+B)  + Sin (A-B)  y (x, t)  =  2  Sin (π x)     Cos (100 π t)                 =  Sin (πx + 100πt)    +    Sin  (πx - 100 πt)                 =  Sin (πx + 100πt)    -    Sin  (100πt  -  πx )                 =  Sin (100 πt + πx)   +  Sin  (100 πt  -  πx + π)GENERAL formula  for a standing wave :  y (x, t) = A Sin (ω t - k x + Ф)  these are the component waves which are PART of the stationary wave.component wave 1:    y1 (x,t)  =  sin (π  x  +  100 π t)       angular frequency = ω    = 100 π  radians/sec      frequency = f  = 50 Hz = ω/2π              Time period: 1/f = 0.02 Sec.       Amplitude = A = 1 m       wave number  k =  - π  rad/meter                       we have formula   ω = k V           velocity  v =  ω / k  = - 100 meters/sec          wavelength λ =  v / f  =  100/50  meters =  2 meters  this component of the wave is traveling in the negative x direction. so its velocity is negative. ==========================component wave 2:    y1 (x,t)  =  sin ( 100 π t - π x +  π )       angular frequency = ω    = 100 π  radians/sec      frequency = f  = 50 Hz = ω/2π              Time period: 1/f = 0.02 Sec.       Amplitude = A = 1 m       wave number  k =  π  rad/meter                       we have formula   ω = k v           velocity  v =  ω / k  = 100 meters/sec          wavelength λ =  v / f  =  100/50   meters =  2 meters   INITIAL phase angle = π radians this wave is traveling in the positive x direction.  so  k and v are positive.But the waves are have a phase difference also.

13.

What is heat energy ?

Answer»

a form of energy that causes the SENSATION of hotness or coldness.The energy transferred from one body to ANOTHER when in contact due to temperature differences is called HEAT.Heat ALWAYS transfers from a hot body to a COLD body.The amount of heat depends on the amount of matter present in a body.Heat and temperature are not same.

14.

A racing car has a uniform acceleration of 4 m s (power -2).what distance will it cover in 10s after start? with steps

Answer»

m/sec²t = 10  secondsthe CAR STARTS from rest  ,  so  u = 0.the equation of motion is       s =  u t + 1/2  a t²            =  0 +  1/2  4  10²  meters           =  200  meters

15.

A trolley while going down an inclined plane, has an acceleration of 2 cm s(power -2).What will be its velocity 3s after the start?

Answer»

olley has an acceleration  a =  2 cm / sec²      down the INCLINED plane.    its initial velocity  is    U =  0 m/sec.  as it STARTS from rest.   v =  u  +  a  t    =  0 + 2  * t          =  2 *  3  =  6   m /sec     this velocity is along the inclined plane direction.we need to specify the direction as velocity is a vector quantity.

16.

A train is traveling at a speed of 90 km h(power -1).Brakes r applied so as to produce a uniform accelaration of -0.5 m s (power -2).Find how far the train will go before it is brought to rest.

Answer»

kmph  = 90 * 5/18 m/sec = 25 m/seca = -0.5  m/sec²v = 0  as the train COMES to rest.the equation of motion is      v²  =  u² +  2 a s      0  =  25²  -  2 * 0.5 *  s             s =  625 METERS

17.

A bus starting from rest moves with a uniform acceleration of 0.1 s(powrer-2) mins. Find a) the speed acquired b) the distance travelled.

Answer»

/SEC  as it STARTS from REST.   a =  0.1  m/sec²  v =  u +  a  t    =    0.1 t    meters/sec  s =  u t + 1/2  a  t²   =  0.05 t²    meterswe can calculate the speed and DISTANCE travelled after a time interval of t seconds,  if we know  the VALUE of  t.

18.

Calculate a wave velocity when a force of 500 acts on a system with mass per unit length 0.25kg/m

Answer»

g the force acting as TENSION in a string;Force, F = 500Nlinear MASS DENSITY, μ = 0.25 kg/mv = ?

19.

A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is 10 m/s in the downward direction , what will be the height attained by the stone and how much time will it take to reach there? please reply, waiting.......

Answer»

v=0 and U is negative⇔v=u + gt⇔so time is 0.02 seconds0= - 5 + (-10) * TWE KNOW that v^2-u^2=2as or 2ghso 0² - (- 5)² = 2 * (10) * h⇒h = 1.25m

20.

Why a pace bowler runs in from a long distance before he bowls

Answer» STANCE means the bowler will GET more MOMENTUM which will be transfered in the ball and it will have more PACE
21.

Does the surrounding air become warm or cool when vapour phase of H2o condenses?explain?

Answer»

unding air become warm when vapour PHASE of water condenses.2)vapour phase of water are the slower moving molecules in the air.3)removal(CONDENSATION) of slower moving molecules from the surroundings INCREASES the AVERAGE kinetic energy of the REMAINING molecules4) hence, the warming.

22.

in a given species of tobacco there is 0.1mg of virus per c.c.the mass of virus is 4x10000000 kg per kilomole.the number of the molecules of virus present in 1 c.c. will be? plz explain with solution

Answer»

virus = 4×10⁷ kg per kilomoleso mass of 1000 moles virus = 4×10⁷ kgso mass of 1 MOLE virus = 4×10⁷/1000 =  4×10⁴ kgmass of virus in 1CC tobacco, = 0.1mg0.1mg = 1×10⁻⁷ kg4×10⁴ kg contains 1 mole of virus1 kg will have = 1×10⁻⁷ kg will have = number of viruses in 1 mole = 6.022×10²³ virusesnumber of viruses in  mole = So number of viruses PRESENT in 1 cc will be 1.505×10¹².

23.

at a given volume and temperature the presure of a gas will vary 1.directly proprtional to the mass of a gas 2.inversely proportional to mass of gas 3.linearly as the square of the mass of the gas 4.inversely as the square of the mass. please explain your answer

Answer» AL gas law is given as PV=nRT where P = pressureV = volumen = number of moles of gasR = a constantT = temperatureGiven that V and T are constant. So P is directly PROPORTIONAL to n.Since MASS of the gas is directly proportional to number of moles of gas, Pressure will vary directly proportional to mass of gas.Answer is (1).
24.

What is the difference between regular reflection and irregular reflection

Answer»

ys of light strikes a plane surface(mirror) it is REFLECTED in a particular and straight manner it is known as REGULAR reflection.When rays of light strikes a ROUGH surface(road,ETC.) it is not reflected in a particular way and it is in a scattered manner. This is known as irregular reflection.

25.

at constant volume,temperature is increased then----1.collision on walls will be less 2.number of collisions per unit time will increase 3.collisions will be in straight line 4.collisions will not change

Answer»

r of collision per unit TIME will increase.Temperature always increase randomness.As we increase temperature ,then we will provide energy to MOVING particle.That energy is USED to increase its KINETIC energy.Hence its no. of collision per unit time  will increase.

26.

Plzzzzzzzz "help" vt and dt graph of quadratic

Answer»

ave a displacement s as          s  =  u  t  + 1/2 a t²    s = DISTANCE or displacement after  time t SEC.  u  = INITIAL velocity    m/sec   a = UNIFORM acceleration  over time  t    of  m/sec/sec  v = velocity of the particle at time t.then  we have    v =  u +  a  tthe graphs for a uniform    POSITIVE acceleration are  shown  along with the graphs for a uniform velocity.   example acceleration  =  5 m/sec/sec            u = 10 m/sec

27.

Report why dogs pant during the hot summer days with the concept of evaporation

Answer» ORATION RATE is high when SURFACE area is more.2) dogs have toungues with large surface area.3)so, when dogs pant evaporation takes place it PROVIDES them cooling effect.4)evaporation is a cooling process.
28.

The Dead Sea lies about 1300 feet below sea level and is the lowest place on the Earth's surface.How would the air pressure at the Dead Sea affect the boiling point of water?

Answer»

ead sea is much below the sea level, the ATMOSPHERIC pressure is more at that level than NORMAL atmospheric pressure at sea level. Since, BOILING point of WATER increases with increases in AIR pressure, the boiling point will increase.

29.

What is si unit of mass

Answer» UNIT of MASS is KILOGRAM (KG).
30.

A spring mass system is characterized by K=16N/m and m= 1.0kg. System is oscillate with an amplitude of 0.20m.(1)Calculate the angular frequency of oscillation (2) obtain an expression for the velocity of the block. As a function of displacement

Answer»

g mass system  is CHARACTERIZED by the equation of motion:        m a = F = m d² X / d t² = - k x                      d² x/ d t² = - k/m  x  = - ω₀² xthe solution for displacement at time t is given by  :                     x = A Cos (ω₀ t + Ф)   ω₀ is the natural frequency of the system for simple harmonic motion.         =  √(k/m) = √(16/1) = 4 rad /SEC.      angular frequency is 4 rad /sec.  A = AMPLITUDE of the vibration = 0.20 metes.  Ф = initial phase of the system, given by          Cos Ф = x₀ / A ,  where x₀ = the position of mass from the mean position when the oscillation has started.      displacement x = A Cos (ω₀ t + Ф)   differentiate :  dx/dt = v = velocity of mass m at time t          v = - A * ω₀  sin (ω₀ t + Ф)    v = -  0.20 * 4 Sin (ω₀ t + Ф)        v = dx/dt = - 0.80 Sin 4 t      if  the initial phase = 0°.

31.

What is displacement

Answer»

acement is the shortest DISTANCE from the initial to the final POSITION of a POINT.

32.

Technology behind the hitler's stealth fighter plane??

Answer»

s STEALTH Fighter reveals NAZI Germany's top-secret development of radar-evading technology.In the final months of World War II a jet powered flying wing made its first test flight from a REMOTE airfield deep inside Nazi Germany. Generations ahead of its time, the Horten 229 had been designed to be a lethal fighter-bomber and more importantly, virtually undetectable to ALLIED radar. Had Reimar and Walter Horten designed the world’s first stealth fighter? Hitler's Stealth Fighter goes behind the scenes with an elite group of aerospace engineers and stealth experts from Northrop Grumman as they build a full-scale model of the sinister bat wing fighter. Once complete, go where cameras have never been ALLOWED as the stealth's Northrop team test the Nazi fighter’s capability at their remote Tejon Radar Range. After decades of debate and speculation the mystery of the Horten 229’s stealth capability is finally put to rest.

33.

The specific resistance of a wire is "rho" ,its volume is 3m3 and its resistance is 3 ohm, then its length will be a.underroot 1/ rho b. 3/ underroot rho c.1/ rho * underroot 3 d. rho * underroot 1/3

Answer»

of wire V = length L * area of cross SECTION A         A = V/Lρ = resistivity of the material.Resistance of a wire R = ρ L / A = ρ L² / V         L² =  V R / ρ  = 3 m³ * 3 Ω /ρ       L = 3/√ρ the OPTION is B.

34.

A body of mass 0.2 kg is suspended from a spring of force constant 80 Nm−1 . A damping force is acting on the system for which γ = 4 Nsm−1 . Write down the equation of motion of the system and calculate the period of its oscillations. Now a harmonic force F =10cos10t is applied. Calculate a and θ when the steady state response is given by a cos(ωt − θ).

Answer»

kgSpring restoration force F = - k x ,    k = 80 N/mDamping force  F_d = -b v  ,    where  b = 4 N-sec/meter     F = - k x - b v      --- (1)     m a = m d² x / d t²  = - k x - b v       d² x /d t²  = -k/m x - b/m dx/dt            --- (2)   This is the equation of motion in the form of DIFFERENTIAL equation.            let     x = A e^{-a x}  Sin (ωt+Ф)      --- (3)                                 we need to determine A, a, and ω.  differentiate two times:         dx/dt = - a A e^{-a x} Sin ωt + Aω e^{-a x}  Cos ωt        -- (4)                 = A e^{-a x}  [ - a Sin ωt + ω Cos ωt ]       d² x/d t² =  a² A e^{-a x} Sin ωt - a A ω e^{-a x} Cos ωt                              - Aaω e^{-a x} Cos ωt - Aω² e^{-a x} Sin ωt                = (a² - ω²) A e^{-a x} Sin ωt  -  2 A a ωe^{-a x} Cos ωt        ---- (5)  -kx/m - b/m * dx/dt  = -k/m A e^{-a x} Sin ωt  - b/m A e^{-ax} [- a Sin ωt + ω Cos ωt ]                        = A e^{-ax} Sin ωt [ -k/m + ab/m ] - bω/m A e^{-ax} Cos ωt    --- (6)COMPARE equations (5) and (6), we get :           (ab-k)/m = (a² - ω²)    -- (7)           2 a = b/m     =>     b = 2 a m         -- (8)                  =>  2 a² - k / m = a² - ω²         =>  ω² = (k/m  - a²)    x =  A e^{- a x }  Sin [ √(k/m - a²) t  + Ф ]===========================m = 0.2 kg ,    k = 80 N/m    and    b = 4 N-sec/m                   b = 2 a m    =>  a = 10 units  angular frequency ω = √ (k/m - a²) = √(400- 100) = 10√3 rad/sec     frequency = 5√3/π  Hz     and  time period = T = 1/f = π /(5√3) sec = 0.362 secThis is the dampened frequency of the spring mass system.Natural frequency = ω₀ = √(k/m) = √(80/0.2) = 20 rad/sec===============================when a force of  F = 10 Cos 10 t  = F₁ Cos (ω₁t) s applied, The natural frequency of the force and the system are different.  This is a case of forced oscillations.  net force = m a = - k x - b v + 10 Cos 10t      --- (9)      m d²x/dt² = - k x - b dx/dt + 10 Cos 10t     steady state response :  x = a Cos (ω₁ t - Ф),  where,         ω₁ = frequency of the EXTERNAL force = 10 rad/sec.       so frequency = f₁ = 10/2π = 5/π Hz  and the time period T₁ = π/5 Sec.       ω₀ = natural freuency of the spring with out damping or external force = √(k/m)             = 20 rad /sec          a = AMPLITUDE =           Ф = phase =

35.

In a series LCR circuit, L = 10 mH, C = 1 µF and R = 0.4 Ω. i) Write the equation of motion when the charged capacitor discharges and discuss the nature of the discharge. ii) Will it be oscillatory or dead beat? iii) How long does the charge oscillations take to decay to half its initial value.

Answer»

the capacitor is charged to Q₀  at  t= 0.We have  L = 10 mH ,     C = 1 μF    ,     R = 0.4 ΩWhen at t =0, the circuit with L , C, and R is closed, then the capacitor STARTS to discharge.  The current starts to flow in inductor and stores energy in it.  Some energy starts dissipating through  R.sum of  potential diff, is 0 in the circuit.  let I be the current in the circuit.          L d I / dt  + Q/C  + R I  = 0          differentiate wrt t, and divide by L      d² I /d t² + I / LC + R/L  d I / dt = 0            ---- (1)   let  b = R = 0.4Ω ,    ω₀² = 1/LC  =  k/m,   so  k =1/C = 10⁶ F⁻¹  ,and    m = L = 10 mH   So we have  ω₀ =  10⁴ rad/sec    ,  f = 10⁴/2π  Hz then        d² I/ dt² +  b/m  d I / dt  +  ω₀²  I  =  0        this is the equation.              This looks exactly like the equation for a damped oscillator, with a natural frequency = ω₀.   we know the solution :  I (t) = I₀  e^{- R/2L t }  Sin (ω' t + Ф')         where    ω'  =  √[ ω₀² - (R/2L)² ]  = √ [ 10⁸ - 20² ]  = 9999.98 rad/sec           as   R/2L is  < <  ω₀,  the circuit will OSCILLATE as a slow damped circuit.                   (condition :  R < 2 √[L/C]  same as above)      So  I (t) = I₀  e^{- R/2L t }  Sin (ω' t + Ф')                          I (t = 0)  = I₀ Sin Ф'    where    I₀ =            Cos Ф' = b/(2m ω₀) =  R / (2 L ω₀)  = 20/10000 = 0.002                 Ф' = 1.568 radians  or  89.88 deg.======Quality factor of the circuit is =  Qf =  √[L/C] / R  =  ω₀ / (b/m)  = ω₀ / (R/L)           =  250 approximatelyQf  gives an indication of  number of - minimum - cycles that oscillations will take place, before the amplitude becomes low.========================      d Q(t) / dt  =   I (t) = I₀  e^{- R/2L t }  Sin (ω' t + Ф')we use the integration by parts:  u = e^{- R/2L t }        V ' = Sin (ω' t + Ф')                v = - 1/ω'  Cos (ω' t + Ф')  Q(t) = - 1/ω'  e^{- R/2L t } Cos(ω' t+Ф') -  R/(2Lω')   integral  e^{- R/2L t } Cos (ω' t + Ф')        = - 1/ω'  e^{- R/2L t } Cos(ω' t+Ф') - R/(2Lω')  [ e^{- R/2L t } Sin (ω' t + Ф')                        -  R/(2Lω')  integral e^{- R/2L t } Sin (ω' t + Ф')  ]        =  - 1/ω'  e^{- R/2L t } Cos(ω' t+Ф') - R/(2Lω')  e^{- R/2L t } Sin (ω' t + Ф')                      + R²/(4L²ω'²)  Q(t)Q(t) [ 1 - R²/(4L²ω'²) ]  = - 1/ω'  e^{- R/2L t } Cos(ω' t+Ф') - R/(2Lω')  e^{- R/2L t } Sin (ω' t + Ф')Q(t) = - 1/ω'  e^{- R/2L t } [ Cos(ω' t+Ф') + R/(2L) Sin (ω' t + Ф') ] / [ 1 - R²/(4L²ω'²) ]Q(0) =  - 1/ω' [ Cos Ф'  + R/2L Sin Ф' ] / [ 1 - R²/(4L²ω'²) ] we want  time  t  such that  the amplitude is HALF of Q(0).

36.

Establish the equation of motion of a damped oscillator and show that for a weakly damped oscillator, the displacement is given by ( ) exp( )cos( ) x t = a0 −bt ωd t + φ where symbols have their usual meanings.

Answer»

take a spring mass system with a natural frequency ω0. m = mass of the body oscillatingSpring restoration force F = - k x ,      k = spring constant.Damping force  F_d = - b v  ,    where  b = damping factor.x = displacement.v = velocity of mass.ω₀ is the frequency of the spring mass when there is no damping.  Only force is spring force.  so,      m d² x / d t²  = - k x    has the solution:                      x = A0 Sin (ω₀ + Ф₀)             --- (0)                       and  ω₀ = √(k/m)       or  ω0² = k/m     ---- (12)===========================    net force acting on mass m is:   F = - k x - b v      --- (1)              The minus sign is because spring restoration force is OPPOSITE to displacement direction and the damping force is in the direction opposite to velocity.               m a = m d² x / d t²  = - k x - b v               d² x /d t²  = -k/m * x - b/m * dx/dt            --- (2)   This is the equation of motion in the form of differential equation. The general solution for the above differential equation is in the following form:           let     x = A_t e^{-at}  Sin (ω' t + Ф')      --- (3)                                 we need to determine A_t, a, and ω'.  differentiate two times:         dx/dt = - a A_t e^{-at} Sin (ω't+Ф')+ + A_tω' e^{-a x}  Cos (ω't+Ф')     -- (4)                 = A_t e^{-at} [ - a Sin ω't + ω' Cos ω't ]      d² x/d t² =  a² A_t e^{-at} Sin (ω't+Ф') - a A0 ω' e^{-at} Cos (ω't+Ф')                              - A_t a ω' e^{-at} Cos (ω't+Ф') - A_t ω'² e^{-at} Sin (ω't+Ф')            = (a² - ω'²) A_t e^{-at} Sin (ω't+Ф')  -  2 A_t a ω'e^{-at} Cos (ω't+Ф')  --(5)Find the RHS of equation (2)   -kx/m - b/m * dx/dt       = -k/m A_t e^{-at} Sin(ω't+Ф') - b/m A_t e^{-at} [- a Sin(ω't+Ф') + ω' Cos(ω't+Ф')]       = A_t e^{-at} Sin(ω't+Ф') [ -k/m + ab/m] - bω'/m A_t e^{-at} Cos(ω't+Ф') --(6)Compare equations (5) and (6), we GET :           (ab - k) / m = (a² - ω'²)    -- (7)            a = b/(2m)     =>     b = 2 a m         -- (8)         =>  2 a² - k / m = a² - ω'²         =>  ω'² = ( k/m  - a²)  = (ω₀² - a²) =  [ω₀² - b²/4m² ]            =>   ω' = √[ω₀² - b²/4m² ]           --- (9)  also the phase angle of the damped oscillation is :          Cos Ф' = a/ ω₀ = b/(2m ω₀)         Tan Ф' = ω'/a = √[ 4m² ω₀²/ b² - 1 ] = √[ ω₀²/a² - 1 ]      --- (10) in terms of initial value of  displacement x = x₀ at t = 0sec and initial velocity v₀ = dx/dt at t = 0sec of the damped oscillations,          Tan Ф' =  ω' x₀ / [ v₀ +  a x₀ ]          x =  A_t  e^{ -bt /(2m) }  Sin [ ω' t  + Ф' ]      -- (11)                      A_t  = x₀ Cosec Ф'    from EQ (3)                    =  √ [ x₀² + (v₀ +  a x₀)² / ω'²  ]

37.

A spring mass system is characterized by 1 16Nm− k = and m = 0.1 kg.The system is oscillating with an amplitude of 0.20 m. i) Calculate the angular frequency of oscillation. ii) Obtain an expression for the velocity of the block as a function of displacement and calculate its value at x = 1.0 m. iii) Also calculate energy of the spring-mass system.

Answer»

n of motion and force:           F = m a = m d²x/dt² = - k x                      d²x/dt² = - k/m x      let x = A Sin (ωt + Ф)             then  d²x/dt² = - A ω² Sin(ωt+Ф) = - ω² x       k = 116 N/m  or  16 N/m  ???      which ONE ?       m = 0.1 kg       A = 0.20 metersSHM :  angular frequency = ω = √(k/m) = √(116/0.1) = 34 rad/sec                         if  k = 16 N/m,    ω = √160 = 4√10 rad/sec   ==========     x = A Sin (ωt + Ф)          = displacement from the mean POSITION     v = velocity of the particle executing the SHM     v = dx/dt = A ω Cos (ω t + Ф)            v  = ω  √A² - x² )  = ω A  √[1 - x²/A² ]====================   x = 1.0 m      this value is not possible, as  amplitude is 0.20 m.  SO x has to be less than 0.2 m.  Is it 0.1 meters ?      x has to be less than or EQUAL to amplitude.   v = 4√10 rad/sec * √[0.2² - 0.1²] meters = 2.19 m/sec========================Energy of the spring MASS system :        = 1/2 m v² at the mean equilibrium position , as x = 0  and PE = 0         = 1/2 k A²  at the extreme position when x = A, as  v = 0 and KE = 0.     = 1/2 * 0.1 kg * 0.20² = 0.002 Joules

38.

What is the exact speed of light in vacuum ?

Answer» CT SPEED of light in vacuum 186,282 MILES PER second .......
39.

The resistence in a wire is directly proportional to ...............?

Answer»

istence in a WIRE is DIRECTLY PROPORTIONAL to LENGTH of wire.

40.

Why mosquitoes dont eat anything else rather than sucking blood

Answer» LY MOSQUITOES dont feed only on BLOOD but also feed on nectar and water. only female mosquitoes SUCK the blood and USE the iron and protien in them to produce the eggs.
41.

What do you mean resistivity and resistance?

Answer»

vity values are USED to COMPARE the conducting properties of different materials.resistance, is independent of the DIMENSIONS of the SAMPLE.

42.

A force of 20N acts on a body of mass 4kg at rest. What is the accelaration of the body? What is the velocity after 10sec if the same force acts? After 10sec if the force ceases to act how will the body move?plz urgentttttttttttttt

Answer»

F = 20 NewtonsMass = m = 4 kginitial velocity u = 0 ACCELERATION a = force / mass = F / m         = 20 / 4 = 5 meters/sec²velocity v = u + a t     v = 0  + 5 m/sec² * 10 sec = 50 m/sec  During the first 10 SECONDS when the force is acting on the body, the body ACCELERATES continuously.  That is its speed increases every instant.  At 1 sec its speed is 5 m/s,  at 2 sec, its speed is 10 m/s,  at 3 sec, its speed is 15 m/s ....   when the force ceases to act at 10 sec, then the body CONTINUES to MOVE along the straight line (as per the 1st law of Newton).  it moves with a constant velocity of 50 m/sec.  this is the inertia of motion.

43.

How do animals emit sonar radiation?

Answer»

e a variety of ultrasonic ranging (ECHOLOCATION) techniques to detect their prey. They can detect frequencies beyond 100 kHz, possibly up to 200 kHz.[6]Many insects have good ultrasonic hearing and most of these are nocturnal insects listening for echolocating bats. This includes many groups of moths, beetles, praying mantids and lacewings. Upon hearing a bat, some insects will make evasive manoeuvres to escape being CAUGHT.[7] Ultrasonic frequencies trigger a reflex action in the noctuid moth that cause it to drop SLIGHTLY in its flight to evade attack.[8]Tiger moths also emit clicks which may disturb bats' echolocation,[9][10] but may also in other cases evade being eaten by advertising the FACT that they are poisonous by emitting sound.[11][12]

44.

Information about the history of spherical mirrors in human civilization

Answer»

r still or dark water collected in a vessel was considered or used as mirrors by ancient people. Then as days passed obsidian mirrors came in to existence followed by metal coated glass mirrors this led to discovery of metal coated spherical or parabolic mirrors.  A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. There are TWO types of spherical mirrors: concave, and convex. These mirrors are also known as parabolic mirrors discovered in mid9th century Ibn al haytham and Ibn sahl.parabolic mirrors were described in classical antiquity written by mathematician-Diocles . In addition to these RESEARCHES Ptolemy also carried out experiments with curved polished iron mirrors and discussed about convex spherical and concave spherical mirrors in his book OPTICS.   Inspite of these researches finding the focal length of spherical mirror was a though task but finally Ibn al Hay tham got a break through by finding out the focal length of curved surfaces USING the laws of reflection.he stated that “All the reflected rays of a mirror converge or diverge and meet at a point known as focus and the distance between focus and pole of mirror is known as focal point of mirror.’’Also many scientists came to a conclusion that spherical mirrors can be divided into concave and convex mirrors.   Spherical mirrors   Concave mirrors   Convex mirrors The invention of concave and convex mirrors led to many changes and have become a part of our life .

45.

How can u diferentiate heat from temperature?

Answer»

a fundamental difference between temperature and heat. Heat is the amount of energy in a SYSTEM. The SI units for heat are Joules. A Joule is a Newton times a meter. A Newton is a kilogram-meter per second squared. Heat is transferred through radiation, conduction and convection. The amount that molecules are vibrating, rotating or moving is a direct function of the heat CONTENT. Energy is transported by conduction as molecules vibrate, rotate and/or collide into each other. Heat is moved along similar to DOMINOS knocking down their neighbors in a chain reaction. An increase of electromagnetic radiation into a system causes the molecules to vibrate, rotate and/or move faster. With convection, higher energy molecules are mixed with lower energy molecules. When higher energy molecules are mixed with lower energy molecules the molecular motion will come into equilibrium over time. The faster moving molecules will slow down and the slow moving molecules will speed up. Temperature is the MEASURE of the AVERAGE molecular motions in a system and simply has units of celsius,KELVIN Notice that one primary difference between heat and temperature is that heat has units of Joules and temperature has units of (degrees F, degrees C, or K). Another primary difference is that energy can be transported without the temperature of a substance changing (e.g.latent heat), ice water remains at the freezing point even as energy is brought into the ice water to melt more ice). But, as a general statement (ignoring latent heat), as heat energy increases, the temperature will increase. If molecules increase in VIBRATION, rotation or forward motion and pass that energy to neighboring molecules, the measured temperature of the system will increase.NOTE:THE TEXT IS NOT COPIED FROM ANYWHERE.IF IT HELPS U PLZZZZZZZZ MARK IT AS BST

46.

Is work done when ant sits on the back of a mice and the mice carries the ant for a distance of 10m

Answer»

E DOESNOT HAPPENS ON THE ANT SINCE IT DOESNOT HAVE ANY DISPLACEMENT WHILE IT SIT ON THE BACK OF THE MICE SO      W=F*S        =F*0  [S=0]       =0

47.

What is meant by ultrasonic sound and infosonic sound and give some examples?

Answer» NIC:they are WAVES below 60hzinfrasonic:they are waves above 60000hz
48.

What force is responsible for taking out butter from milk?

Answer»

ugal force is HELPFUL in SEPARATING BUTTER from MILK.

49.

Young's modulus elasticity of steel is 19×10 raise to power 10 Newton/m2 into dyne/m2 1 NEWTON=100000 DYNE its urgent......

Answer» YOUNG's modulus is N/m^2Therefore, its dimensions = (Force)/(Distance)^2[Y] = [MLT^-2]/[L^2] = [ML^-1T^-2]                  1N/m^2 = (1KG) (1m^-1) (1s^-2)                  1 dyne/cm^2 =(1g) (1cm^-1) (1s^-2)THEREFORE, 1N/m^2/1dyne/cm^2 = (1kg/1g) (1m/1cm)^-1 (1s/1s)^-2                                              = (10^3g/1g) (10^2cm/1cm)^-1 (1)^-2                                              = 1000 * 1/100 * 1                                              =10 So, 1N/m^2 = 10 dyne/cm^2Hence,19*10^10 Newton/m^2 = (19*10^10)*10 dyne/cm^2 = 19 X 10^11 dyne/cm^2
50.

a taxi driver noted the reading on the odometer as 11185 km when he started the journey .after 30 minutes drive, he noted that the odometer reading is 11200 km. find the average speed

Answer»

e traveled = (11200-11185) KM = 15 kmTime taken = 30 MINUTES = 30/60 HR = 0.5 hrSpeed = Distance/Time = 15/0.5 = 30 km/hr