# 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: 1. ${m}_{1}:{m}_{2}:{m}_{3}$ 2. ${m}_{1}:2{m}_{2}:3{m}_{3}$ 3. 1 : 1 : 1 4. $\frac{1}{{m}_{1}}:\frac{1}{{m}_{2}}:\frac{1}{{m}_{3}}$

Subtopic:  Work Energy Theorem |
79%
From NCERT
AIIMS - 2002
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When a body moves with a constant speed along a circle

(1) No work is done on it

(2) No acceleration is produced in the body

(3) No force acts on the body

(4) Its velocity remains constant

Subtopic:  Work Done by Variable Force |
71%
From NCERT
PMT - 1994
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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

(1) 0

(2) $\left(\frac{m{v}^{2}}{l}\right) . 2\pi l$

(3) $\text{mg\hspace{0.17em}.\hspace{0.17em}2πl}$

(4) $\left(\frac{m{v}^{2}}{l}\right) . \left(l\right)$

Subtopic:  Work Done by Variable Force |
80%
From NCERT
PMT - 1993
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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

(1) $\sqrt{2gR}$

(2) 2gR

(3) $\sqrt{3gR}$

(4) $\sqrt{gR}$

Subtopic:  Work Energy Theorem |
72%
From NCERT
PMT - 1979
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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:

(1) gl

(2) 2 gl

(3) $\sqrt{gl}$

(4) $\sqrt{2gl}$

Subtopic:  Work Energy Theorem |
75%
From NCERT
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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

(1) 2 mg

(2) mg

(3) 3 mg

(4) $\sqrt{3}mg$

Subtopic:  Work Energy Theorem |
53%
From NCERT
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As per the given figure to complete the circular loop, what should be the radius of the loop?

1. 4 m
2. 3 m
3. 2.5 m
4. 2 m

Subtopic:  Work Energy Theorem |
61%
From NCERT
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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

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

(2) $2as{\left(1+\frac{{s}^{2}}{{R}^{2}}\right)}^{1/2}$

(3) 2 as

(4) $2a\frac{{R}^{2}}{s}$

Subtopic:  Concept of Work |
52%
From NCERT
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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

(1) 20 m/sec

(2) $10\sqrt{3}m/\mathrm{sec}$

(3) $5\sqrt{2}\text{\hspace{0.17em}}m/\mathrm{sec}$

(4) 10 m/sec

Subtopic:  Work Energy Theorem |
59%
PMT - 1990
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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

Subtopic:  Work Energy Theorem |
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