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Question

A ball is rolling without slipping in a spherical shallow bowl (radius R) as shown in the figure and is executing simple harmonic motion. If the radius of the ball is doubled, the period of oscillation
631323_7e046cd6268a464da4dd9765da4b537a.jpg

A
Increases slightly
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B
Is reduced by a factor of 1/2
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C
Is increased by a factor of 2
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D
Decreases slightly
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Solution

The correct option is D Decreases slightly
a=gsinθ1+Imr2=5gsinθ7
α=5gsinθ7r
now we will calculate the angular velocity about center of sphere
ω=ωrRr
α=αrRr
α=5gsinθ7(Rr)
T=2π7(Rr)5g
hence wih increase in r, T will decrease.

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