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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))`
`implies a = (5)/(7) (g sintheta )/( R -r)`
`omega = sqrt((5g)/(7(R-r))`
` = T = 2pi sqrt( 7(R-r))/(5r)`
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