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Question

A ball of mass 500 g is initially at rest at the bottom most point of a smooth vertical circular track of radius 10 m. For looping a loop, the minimum kinetic energy the ball should have at the bottommost point on the track is

A
100 J
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B
125 J
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C
250 J
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D
1250 J
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Solution

The correct option is B 125 J
Let the velocity of the ball at the bottom of the track be vA

The minimum velocity at the bottom for completing the loop is given by,
vbottom=vA=5gl

vA=5×10×10=105 m/s

Hence the minimum kinetic energy at the bottom most point on the track is given by,
K.E=12mv2A=12×0.5×(100×5)

K.E=125 J

Hence option B is the correct answer.

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