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How many time constants will elapse before the power delivered by the battery drops to half of its maximum value in an RC circuit ?

A plane surface is inclined making an angle $\theta$ with the horizontal. From the top of this inclined plane, a bullet is fired with velocity $v$. The maximum possible range of the bullet on the inclined plane is

If potential energy between a proton and an electron is given by $U=\frac{-k{e}^2}{2R^3}$, where e is the charge of electron and R is the radius of atom, then radius of Bohr's orbit is given by ($h$ = Planck's constant, $k$ = constant)

Two discharge tubes have idential material structure and the same gas is filled in them. The length of one tube is 10 cm and that of the other tube is 20 cm. Sparking starts in both the tubes when th epotential difference between the cathode and the anode is 100 V. If the pressure in the shorter tube is 1.0 mm of mercury, what is the pressure in the longer tube?

200 gm of a solid ball at ${20}^{0}C$ is dropped in an equal amount of water at ${80}^{0}C$. The resulting temperature is ${60}^{0}C$. This means that specific heat of solid is

A particle is moving on a circular path of 10 m radius. At any instant of time, its speed is 5 m/s and the speed is increasing at a rate of $2m/s^2$. The magnitude of net acceleration at this instant is:

A uniform solid cylinder of mass 'm' can rotate freely about its axis which is kept horizontal. A particle of mass $m_0$ hangs from the end of a light string wound round the cylinder. When the system is allowed to move, the acceleration with which the particle descends is

Block $A$ weighs $4kg$ and block $B$ weighs $8kg$. Coefficient of kinetic friction between all surfaces in contact is $0.2$. The force $F$ necessary to drag the block $B$ at constant speed if $A$ is held at rest as shown in the figure is
(Take $g=10m/s^2$)

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length 7.6 m. The diameter of the moon is 3450 km and the distance between the earth and the moon is $3.8\times {10}^5\text{km}$

A body of mass $m$ moves with speed $2v$ and a body of mass $2m$ moves with speed $v$ on a smooth horizontal surface, both along positive $x$ axis. After some time, they collide and stick together. What is the speed of the system after they stick together?

A bullet of mass $10\text{g}$ leaves a rife at an initial velocity of $3000\text{m/s}$ and strikes the earth at the same level with a velocity of $2000\text{m/s}$. The work done in overcoming the resistance of air will be

Two cars, initially at a separation of $12\text{m}$, start simultaneously. First car $A$, starting from rest moves with an acceleration $2{\text{m/s}}^2$ , whereas the car $B$, which is ahead, moves with a constant velocity $1\text{m/s}$, away from car $A$ along the same direction. Find the time when car $A$ overtakes car $B$.

Determine the surface tension forces in case a plate of radius 10cm is placed on a water surface (surface tension of water = $7\times {10}^{-2}N/m;\pi =\frac{22}{7})$

If the wavelength of light in an experiment on photo electric effect is doubled,

A body moving in a straight line with constant acceleration of $10{\text{ms}}^{-2}$ covers a distance of $40\text{m}$ in the $4^{th}$ second. How much distance will it cover in the $6^{th}$ second?

The equation of a wave travelling on a string stretched along -axis is given by $(y=A{e}^{-{(\frac{x}{a}+\frac{t}{T})}^2})$
Where is the maximum of pulse located at t=T ?

A double convex lens made of glass $(\mu =1.5)$ has both radii of curvature of magnitude 20 cm. Incident rays parallel to the axis of the lens will converge at a distance L such that:

Kerosene oil rises up in the wick of a lantern because of:

A stone of mass 5 kg is attached to a string of 10 m length and is whirled in a horizontal circle. The string can withstand a maximum tension of 160 N. The maximum velocity of revolution that can be given to the stone without breaking the string is

Two fat astronauts each of mass 120 kg are travelling in a closed spaceship moving at a speed of 15 km/s in the outer space far removed from all other material objects.The total mass of the spaceship and its contents including the astronauts is 660 kg.If the astronauts do slimming exercise and thereby reduce their masses to 90 kg each,with what velocity will the spaceship move?

A long thread suspended from a fixed point has a small mass swinging to and fro at its lower end. Which of the following statement is correct?

a. The potential energy of the mass is maximum in the middle of the swing

b. The kinetic energy is maximum in the middle of the swing.

c. The potential energy is always equal to the kinetic energy.

d. The potential energy and the kinetic energy is same in the middle of the swing.

A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats

per second. The beat frequency does not change if the length of the wire is

changed to 21 cm. the frequency of the tuning fork (in Hertz) must be

[UPSEAT 2000; Pb. PET 2004]

A tangential force $\left(F\right)$ is applied on the surface of the cuboidal box as shown in figure. Find out the shearing strain.

The area of the region in the first quadrant enclosed by the x-axis and the line $x=\sqrt{3}y$, the circle $x^2+y^2=4$ is

A particle is projected with an initial speed u form a point at height h above the horizontal plane as shown is the fig. Find the maximum range on the horizontal plane

Two plane mirrors are placed as shown in the figure below:
A point object is approaching the intersection point of mirrors with a speed of 100 cm/s. The velocity of the image of object formed by $M_2$ w.r.to velocity of image of object formed by $M_1$, is

A particle executes S.H.M of amplitude a

1. At what distance from mean position is it's K.E is equal to its P.E

2.At what point is its speed half the maximum speed

If a liquid takes $30\text{s}$ in cooling from ${95}^{\circ }\text{C}$ to ${90}^{\circ }\text{C}$ and $70\text{s}$ in cooling from ${55}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ then temperature of room is -

A man is standing in a valley between two parallel mountains. He fires a gun and hears echo at an interval of 2s and 3.5s. what is the distance between 2 mountains? (Take speed of sound = 350 m/s)

If a constant force acts on a body initially kept at rest the distance moved by the body in time T is proportional to

(A) t (B) t² (C) t³

Please explain why t² i answer.

Categorise canals, houses, schools, railways, ships, hospitals, banks, development banks, aerodromes, courts, power plants, transmission lines and satellites into economic and social infrastructure.

Water flows through a frictionless duct with a cross-section varying as shown in the figure. The pressure $P$ at points along the axis (starting from left end to right end) is represented by

In an a.c. circuit the voltage applied is $E=E_{0}sin\omega t$. The resulting current in the circuit is $I=I_{0}sin(\omega T-\frac{\pi }{2})$ The power consumption in the circuit is given by

A particle moves in a straight line with retardation proportional to its displacement. Its loss in kinetic energy for a displacement ‘x’, is proportional to

The transfer characteristics of a base biased transistor has the operation regions namely, cut off, active region and saturation region. For using the transistor as an amplifier it has to operate in the region:

A longitudinal wave is produced on a slinky toy. The wave travels at a speed of $30\text{cm/s}$ and the frequency of the wave is $20\text{Hz}$. What is the minimum separation between two consecutive compressions of the slinky toy ?

A wheel of radius $r=1\text{m}$ rolls without slipping with an angular velocity of $\omega =\frac{\pi }{4}\text{rad/s}$ about its centre and velocity of its centre of mass is $v_{COM}=2\text{m/s}$. If the point $P(0,0)$ is in contact with the ground initially, find its position vector after time $t=1\text{s}$.

When a capillary tube is dipped in a liquid, liquid rises $0.06\text{m}$ in it. Surface tension of liquid is $0.03\text{N/m}$, density of liquid is ${10}^3{\text{kg/m}}^3$. If contact angle is ${60}^{\circ }$, then radius of capillary is (Assume $g=10{\text{m/s}}^2$)

A ray of light is incident on a plane mirror at an angle ${50}^{\circ }$. The deviation produced by the plane mirror will be

The accleration of a particle is given by $a=(3t^2+2t+2)$ ${\text{ms}}^{-2}$ where $t$ is time. If the particle starts out with an initial velocity $v=2\text{m/s}$ at $t=0$, then the velocity of the particle at the end of $2\text{s}$ is

A body is projected from the top of a tower of height $32\text{m}$ with a velocity of $20\text{m/s}$ at an angle of ${37}^{\circ }$ above the horizontal. The time of flight of the projectile is
(Take $g=10m/s^2$)

On seeing enemy ships at a distance of 125$\sqrt{3}$ m from the shore the cannons start firing fireballs. If the cannons fire at a speed of 50 m/s then at what angle should they aim so they do not miss. Also at what angle can the cannons achieve the maximum distance?