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

Options

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

Answer

D

Explanation

`mgsintheta-F_(r)=ma`
`F_(r)=(2)/(5)mr^(2)(a)/(r^(2))=a=(5gsintheta)/(7R-r)impliesomega=sqrt((5g)/(7(R-r)))`
`impliesT=2pisqrt((7(R-r))/(5r))`