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A ball is rolling without slipping in a ...

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

A

Increases slightly

B

Is reduced by a factor of 1/2

C

Is increased by a factor of 2

D

Decreases slightly

Text Solution

Verified by Experts

The correct Answer is:
D
`mg sin theta- F_(r) = ma`
`F_(r)= (2)/(5) mr^(2) (a)/(r^(2)) rArr a= (5g sin theta)/(7R- r) rArr omega = sqrt((5g)/(7(R- r)))`
`rArr T= 2pi sqrt((7 (R- r))/(5r))`
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