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Question

A circular turntable of radius 0.5 m has a smooth groove as shown in figure. A ball of mass 90 g is placed inside the groove along with a spring of spring constant 102 N/cm. The ball is at a distance of 0.1 m from the center when the turntable is at rest. On rotating the turntable with a constant angular velocity of 102 rad/sec the ball moves away from the initial position by a distance nearly equal to:


A
2×101 m
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B
102 m
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C
101 m
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D
103 m
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Solution

The correct option is B 102 m
Given:

k=102 N/cm or 104 N/m

ω=102 rad/sec

l=0.1 m

m=90 g=901000 kg

At equilibrium, balancing the centripetal force and the force experienced due to the spring:

kx=mω2r

kx=mω2(l+x)

104x=90×103×104(0.1+x)

x=0.09(0.1+x)

x=0.09×0.1+0.09x

x(10.09)=0.09×0.1

x(0.91)=0.09×0.1

x=9.89×103

x=102 m

Hence, Option (B) is the correct answer.

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