Physics - Work Energy Power - Quiz-1

A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is

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84J
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68J
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23J
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8J

Two springs with spring constants $k_{1}$ = 1500 N/m and $k_{2}$ = 3000 N/m are stretched by the same force. The ratio of potential energy stored in the springs will be

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2:1
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1:2
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4:1
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1:4

A block of mass 2 kg moving with velocity of 10 m/s on a smooth surface hits a spring of force constant $80 \times 10^{3}$ N/m as shown. The maximum compression in the spring is

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5 cm
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10 cm
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15 cm
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20 cm

A body starts moving from rest in straight line under a constant power source. Its displacement in time t is proportional to

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$t^{1 / 2}$
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t
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$t^{3 / 2}$
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$t^{2}$

A block of mass m = 25 kg on a smooth horizontal surface with a velocity $\vec{v}$ =3 $m s^{- 1}$ meets the spring of spring constant k = 100 N/m fixed at one end as shown in the figure. The maximum compression of the spring and velocity of the block as it returns to the original position respectively are:

3523

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1.5 m, -3 $m s^{- 1}$
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1.5 m, 0 $m s^{- 1}$
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1.0 m, 3 $m s^{- 1}$
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0.5 m, 2 $m s^{- 1}$

The velocity, given to the block of mass (m), is $\sqrt{\frac{7}{2} g l}$ to rotate it in a circle of radius l. Calculate the height (h) where the block leaves the circle.

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$\frac{3 l}{2}$
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$\frac{4 l}{3}$
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$\frac{5 l}{4}$
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None of these

A spring of force constant 800 N/m has an extension of 5cm. The work done in extending it from 5cm to 15 cm is:

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16 J
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8 J
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32 J
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24 J

If length of string is $l = \frac{10}{3} m, \frac{T_{m a x}}{T_{m i n}} = 4$

$where T_{\max} = Maximum tension in the string T_{\min} = M inimum tension i n the string . Velocity at highest point is -$

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10 m/s
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20 m/s
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$\frac{10}{\sqrt{2}} m / s$
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$10 \sqrt{3} m / s$

The relation between velocity (v) and time (t) is $v \propto \sqrt{t}$ , then which one of the following quantity is constant?

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Force
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Power
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Momentum
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Kinetic Energy

A particle is moving on the circular path of the radius (R) with centripetal acceleration $a_{c} = k^{2} R t^{2}$ . Then the correct relation showing power (P) delivered by net force versus time (t) is

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1
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2
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3
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4

A steel wire can withstand a load up to 2940 N. A load of 150 kg is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position, so that the wire does not break when the load passes through the position of equilibrium, is (2008 E)

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30 $°$
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60 $°$
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80 $°$
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85 $°$

A body is thrown vertically up with a certain initial velocity. The potential and the kinetic energy of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of the potential and the kinetic energies of the body when it crosses at the same point will be:

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1:1
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1:4
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1:7
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1:8

A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F = (x^{2} \hat{j} + y \hat{i}) N$ . The work done by this force will be :

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$\frac{4}{3} J$
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$\frac{5}{6} J$
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$\frac{3}{2} J$
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$\frac{7}{5} J$

A stone is projected from a horizontal plane. It attains maximum height, 'H', and strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall where the ball will strike will be:

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$\frac{H}{2}$
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$\frac{H}{4}$
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$\frac{3 H}{4}$
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None of these

A weightless rod of length 2l carries two equal mass 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in a vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in the horizontal position. The speed of the mass B at the instant rod becomes vertical is:

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$\sqrt{\frac{3 g l}{5}}$
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$\sqrt{\frac{4 g l}{5}}$
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$\sqrt{\frac{6 g l}{5}}$
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$\sqrt{\frac{7 g l}{5}}$

A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

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${Fv}^{2}$
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Fv
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$F / v^{2}$
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F/v

Potential energy (U) related to coordinates is given by U = 3(x + y). Work done by the conservative force when the particle is going from (0, 0), (2, 3) is:

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15 J
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-15 J
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12 J
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10 J

A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [ MP PMT 1993]

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$\sqrt{R g}$
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$\sqrt{2 R g}$
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$2 \sqrt{π R g}$
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$\sqrt{π R g}$

Three different objects of mass $m_{1}, m_{2}$ and m₃ are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of:

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$m_{1} : m_{2} : m_{3}$
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$m_{1} : 2 m_{2} : 3 m_{3}$
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1 : 1 : 1
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$\frac{1}{m_{1}} : \frac{1}{m_{2}} : \frac{1}{m_{3}}$

When a body moves with a constant speed along a circle

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No work is done on it
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No acceleration is produced in the body
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No force acts on the body
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Its velocity remains constant

A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done by centripetal force in full horizontal circle is

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0
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$(\frac{m v^{2}}{l}) . 2 π l$
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$mg . 2πl$
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$(\frac{m v^{2}}{l}) . (l)$

In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be

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$\sqrt{2 g R}$
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2gR
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$\sqrt{3 g R}$
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$\sqrt{g R}$

A ball is suspended by a thread of length l. What minimum horizontal velocity has to be imparted to the ball for it to reach the height of the suspension:

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gl
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2 gl
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$\sqrt{g l}$
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$\sqrt{2 g l}$

A body of mass m hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of 60° with the vertical. The tension in the string at mean position is

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2 mg
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mg
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3 mg
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$\sqrt{3} m g$

As per given figure to complete the circular loop what should be the radius if initial height is 5 m?

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4 m
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3 m

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2.5 m

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2 m

The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as k = as² where a is a constant. The force acting on the particle is

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$2 a \frac{s^{2}}{R}$

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$2 a s {(1 + \frac{s^{2}}{R^{2}})}^{1 / 2}$

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2 as

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$2 a \frac{R^{2}}{s}$

The power of a pump, which can pump 200kg of water to a height of 200m in 10sec is (g = 10 m/s²)

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40 kW

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80 kW

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400 kW

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960 kW

A stone of mass 1 kg tied to a light inextensible string of length $L = \frac{10}{3} m$ is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/sec², the speed of the stone at the highest point of the circle is

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20 m/sec

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$10 \sqrt{3} m / \sec$

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$5 \sqrt{2} m / \sec$

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10 m/sec

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in:
(1)
(2)
(3)
(4) Same in all cases

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1

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2

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3

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4

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is:

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$\sqrt{u^{2} - 2 g L}$

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$\sqrt{2 g L}$

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$\sqrt{u^{2} - g l}$

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$\sqrt{2 (u^{2} - g L)}$

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