(D) For a ball of radius $r$ rolling without slipping in a spherical bowl of radius $R$,the effective length of the pendulum is $(R-r)$.The time perio

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(D) For a ball of radius $r$ rolling without slipping in a spherical bowl of radius $R$,the effective length of the pendulum is $(R-r)$.The time period $T$ of such an oscillation is given by the formula:$T = 2\pi \sqrt{\frac{I_{cm} + mr^2}{mgr^2}} \times \sqrt{R-r} = 2\pi \sqrt{\frac{\frac{2}{5}mr^2 + mr^2}{mgr^2}} \times \sqrt{R-r} = 2\pi \sqrt{\frac{7(R-r)}{5g}}$Since $T \propto \sqrt{R-r}$,if the radius of the ball $r$ is increased,the term $(R-r)$ decreases.Therefore,the time period $T$ decreases slightly.

Class 11 Physics Oscillations Method to determine Time Period and Frequency for diffrent type of Object of SHM

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$A$ 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,then the time period of oscillation

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A
increases slightly
B
is reduced by a factor of $1/2$
C
is increased by a factor of $2$
D
decreases slightly

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Method to determine Time Period and Frequency for diffrent type of Object of SHM

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$A$ 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,then the time period of oscillation

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