Explore topic-wise InterviewSolutions in Current Affairs.

Two particles $P$ and $Q$ describe $\text{SHM}$ of same amplitude $A$, same frequency $f$ along the same straight line. The maximum distance between the two particles is $A\sqrt{2}$. The phase difference between the particle is

Knowing that mass of Moon is $\frac{M}{81}$ where M is the mass of Earth, find the distance of the point where gravitational field due to Earth and Moon cancel each other, from the Moon, Given that distance between Earth and Moon is 60 R. Where R is the radius of Earth

A boat is moving with a velocity $3\hat{i}-5\hat{j}$ with respect to ground. The water in the river is moving with a velocity $-\hat{i}+2\hat{j}$ with respect to ground. The relative velocity of the boat with respect to water is

A particle moves in space along path $z=a{x}^3+b{y}^2$ in such a way that $\frac{dx}{dt}=\frac{dy}{dt}=c$ where a, b and c are constant. Acceleration of particle is

A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle ${60}^o$ with vertical? [$g$ is the acceleration due to gravity]

A composite string is made by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. A transverse wave pulse. $y=\left(6\text{mm}\right)\sin (5t+40x)$, where '$t$' is in seconds and '$x$' is in meters, is sent along the lighter string towards the joint. The joint is at $x=0$. The equation of the wave pulse reflected from the joint is $y=\left(2\text{mm}\right)\sin (5t-40x+\pi )$. The percentage of the power transmitted to the heavier string through the joint is approximately

In the figure shown, the minimum value of the acceleration of wedge ($a$) at which the cylinder starts rising up the inclined surface is

An electric heater is used in a room of total wall area $137m^2$ to maintain a temperature of ${20}^{\circ }C$ inside it, when the outside temperature is - ${10}^{\circ }C$.

The walls have three different layers of materials. The innermost layer is of wood of thickness 2.5 cm, the middle layer is of cement of thickness 1.0 cm and the outer most layer is of brick of thickness 25.0 cm. Find the power of the electric heater. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement and brick are

$0.125W/m^{\circ }C$, $1.5W/m^{\circ }C$ and $1.0W/m^{\circ }C$ respectively.

Two successive resonance frequencies in an open organ pipe are $1954\text{Hz}$ and $2602\text{Hz}$. Find the length of the tube.
[Given, speed of sound in air is $324{\text{ms}}^{-1}$]

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

What is the unit of conductivity and resistivity respectively?

Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same place, (b) if the two waves were produced at the same instant but the first one was produced a distance 4.0 cm behind the second one ? (c) If each of the waves has an amplitude of 2.0 mm, what would be the amplitudes of the resultant waves in part (a) and (b) ?

Two particles $A$ and $B$ projected in the air. $A$ is thrown with a speed of $30\text{m/sec}$ and $B$ with a speed of $40\text{m/sec}$ as shown in the figure. What is the separation between them after $3$ sec?

Force-time$\left(\text{F - t}\right)$ graph of a rocket of mass 1000 kg shown below describes the force on the rocket. Neglecting gravity, the velocity of rocket $16\text{s}$ after starting from rest is

Calculate the Q-value of the fusion reaction

${}^{4}He{+}^{4}He{=}^{8}Be$.

Is such a fusion energetically favourable? Atomic mass of of ${}^{8}Be$ is 8.0053 u and that of ${}^{4}He$ is 4.0026 u.

Figure shows some of the equipotential surfaces of the magnetic scalar potential. Find the magnetic field B at a point in the region.

Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The area around the magnets is divided into four zones.

Given that there is a neutral point, it is located in

A wire has linear resistance $\rho$ (in ohm/m). Find the resistance R between points A and B if the side of the ‘‘big’’ square is d :

A screen is placed $50cm$ from a single slit, which is illuminated with $6000\stackrel{\circ }{A}$ light. If distance between the first and third minima in the diffraction pattern is $3.0mm$, then the width of the slit is

The surface density $\left(\frac{mass}{area}\right)$ of a circular disc of radius a depends on the distance from the centre as $\rho \left(r\right)$ = $A+Br$. Find its moment of inertia about the line perpendicular to the plane of the disc through its centre

An iron tyre is to be fitted on to a wooden wheel of diameter 1 m. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of
(The coefficient of cubical epansion of iron is $3.6\times {10}^{-5}{\left(°C\right)}^{-1}$ and consider iron tyre to be isotropic.)

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is

Two capacitors of capacitance 2C and C are charged to potential difference 2V and V respectively. Now the charged capacitors are connected with a resistor R as shown in figure. Switch ‘S’ is closed at t = 0.

What is the current in circuit as function of time?

A small fish 0.4 m below the surface of a lake, is viewed through a simple converging lens of focal length 2m. The lens is kept at 0.2 m above the water surface such that fish lies on the optical axis of the lens. The image of the fish seen by observer will be at $({\mu }_{water}=\frac{4}{3})$

In the circuit shown, the ideal voltmeter reading is 40 V. The value of unknown resistor R is

A uniformly charged linear rod is placed as shown in the figure. Find the electric field intensity at point P. Given that charge density is $\lambda$ C/m.

Five equal resistaces each of resistance $r$ are connected as shown in figure. A battery of $V$ volt is connected between A and B. The current flowing in AFCEB will be

A rectangular loop $ABCD$ is being pulled out of a magnetic field ${}^{\prime }{B}^{\prime }$ with uniform velocity ${}^{\prime }{v}^{\prime }$ by applying an external force $F$. Length $AB$ is $l$. Length $AD$ is $3l$ and total resistance of the loop is $R$. The thermal power developed in the loop and the force $F$ respectively is

A thin liquid film formed between a $U$ - shaped wire and supports a light weight of $1.5\times {10}^{-2}\text{N}$ (see figure). The length of the slider is $30\text{cm}$ and its weight is negligible. The surface tension of the liquid film is

The position of the particle is given by $x=(e^t-\cos t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to reach the destination which is at a height of 10 m above the point, calculate the work done against friction (negative of the work done by the friction).

In a head on elastic collision of a heavy vehicle moving with a velocity of $10{\text{ms}}^{-1}$ and a small stone at rest, the stone will fly away with a velocity equal to

A park has a radius of 10 m. If a vehicle goes round it at an average speed of 18 km/hr, what should be the proper angle of banking ?

If velocity of a particle is $v\left(t\right)=t^2-5t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $10\text{sec}$ respectively are

A block Q of mass $M$ is placed on a horizontal frictionless surface AB and a body P of mass $m$ is released on its frictionless slope. As P slides by a length $L$ on this slope of inclination $\theta$, the block Q would slide by a distance

A cylindrical vessel containing a liquid is closed by a smooth piston of mass m as shown in the figure. The area of cross section of the piston is A. If the atmospheric pressure is P₀, find the pressure of the liquid just below the piston.

(a) In a liquid with density $1300kg/m^3$, longitudinal waves with frequency 400Hz are found to have wavelength 4m. calculate the bulk modulus of the liquid.
(b) A metal bar with a length of 2m has density $6400kg/m^3$. Longitudinal sound waves take $3.90\times {10}^{-4}$s to travel from one end of the bar to the other. What is Young’s modulus for this metal?

A source of sound $S$ having frequency $f$. Wind is blowing from source to observer $O$ with velocity $u$. If speed of sound with respect to air is $C$, the wavelength of sound detected by $O$ is :

The maximum and minimum of the resultant of two forces are $F$ and $G$ (the angle between these forces is $2\alpha ,$) then, the resultant of $F$ and $G$ is

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

A force applied by an engine of a train of mass $2.05\times {10}^{6}kg$ changes its velocity from 5 m/s to 25 m/s in 5 minutes. The power of the engine is

A metallic sphere of radius R1 carries a charge Q,another uncharged metallic sphere of radius R2 is connected to it using a long wire of negligible resistance. Find the charge transferred from first to second sphere