The velocity, given to the block of mass (m), is 72gl to rotate it in a circle of radius l. Calculate the height (h) where the block leaves the circle.

1. 3l2

2. 4l3

3. 5l4

4. None of these

Subtopic:  Work Energy Theorem |
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If length of string is l = 103m, TmaxTmin=4

where
 Tmax= Maximum tension in the string
Tmin=Minimum tension in the string.
Velocity at highest point is -

1.  10 m/s

2.  20 m/s

3.  102m/s

4.  103 m/s

Subtopic:  Work Energy Theorem |
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The relation between velocity (v) and time (t) is vt, then which one of the following quantity is constant?

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

Subtopic:  Power |
 61%
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A particle is moving on the circular path of the radius (R) with centripetal acceleration ac=k2Rt2. Then the correct relation showing power (P) delivered by net force versus time (t) is 

1. 1

2. 2

3. 3

4. 4

Subtopic:  Power |
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A projectile of mass 50 kg is shot vertically upwards with an initial velocity of 100ms-1. After 5 seconds it explodes into two fragments, one of which having mass 20 kg, travels vertically up with a velocity of 150 ms-1. The velocity of the other fragment at that instant is: [Take g= 9.8 m/s2]

1.  100 ms-1

2.  150 ms-1

3.  -150 ms-1

4.  -15 ms-1

Subtopic:  Collisions |
 52%
From NCERT
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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)

1. 30°

2. 60°

3. 80°

4. 85°

Subtopic:  Work Energy Theorem |
 68%
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A sphere of mass m moving with constant velocity hits another sphere of the same mass at rest. If e is the coefficient of restitution. The ratio of their velocities after the collision is

1.  1 + e

2.  1 + e2

3.  1 + 2e1 - 2e

4.  1 - e1 + e

Subtopic:  Collisions |
 75%
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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: 

1. 1:1

2. 1:4

3. 1:7

4. 1:8

Subtopic:  Conservation of Mechanical Energy |
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A body is displaced from (0,0) to (1m,1m) along the path x=y by a force F=x2j^+yi^N. The work done by this force will be :

1. 43J

2. 56J

3. 32J

4. 75J

Subtopic:  Work Done by Variable Force | Work Energy Theorem | Power |
 73%
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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:

        

1. \(\frac{H}{2} \) 2. \(\frac{H}{4} \)
3. \(\frac{3 H}{4} \) 4. None of these
Subtopic:  Collisions |
 54%
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