# 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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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:

(1) $\sqrt{{u}^{2}-2gL}$

(2) $\sqrt{2gL}$

(3) $\sqrt{{u}^{2}-gl}$

(4) $\sqrt{2\left({u}^{2}-gL\right)}$

Subtopic:  Work Energy Theorem |
From NCERT
PMT - 2004
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The driver of a car travelling at velocity v suddenly sees a broad wall in front of him at a distance d. He should

(1) Brake sharply

(2) Turn sharply

(3) (1) and (2) both

(4) None of the above

Subtopic:  Concept of Work |
From NCERT
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Which of the following graph depicts spring constant k versus length l of the spring correctly

 (1) (2) (3) (4)
Subtopic:  Elastic Potential Energy |
68%
From NCERT
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