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Q.

A uniform disk of mass m and radius R, and uniform solid sphere of mass m and radius R are connected by an ideal spring of stiffness k and lying on a sufficiently rough horizontal surface as shown in figure. If the system is provided a small horizontal disturbance and released, which of the following option(s) is/are correct for the subsequent motion.

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a

Ratio of angular speeds of disk to solid sphere at an instant will be 21/25

b

Time period of oscillation will be $2 π \sqrt{\frac{35 m}{46 k}}$

c

Time period of oscillation will be $2 π \sqrt{\frac{21 m}{29 k}}$

d

Ratio of angular speeds of disk to solid sphere at an instant will be 14/15

answer is A, D.

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Detailed Solution

detailed_solution_thumbnail

Conservation of angular momentum about a point on ground gives

$\begin{array}{l} \frac{3}{2} {mr}^{2} ω_{1} = \frac{7}{5} {mr}^{2} ω_{2} \end{array}$

$\frac{3}{2} {mr}^{2} α_{1} = - k (\frac{29}{17}) x_{1}$

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A uniform disk of mass m and radius R, and uniform solid sphere of mass m and radius R are connected by an ideal spring of stiffness k and lying on a sufficiently rough horizontal surface as shown in figure. If the system is provided a small horizontal disturbance and released, which of the following option(s) is/are correct for the subsequent motion.