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The two torsion pendula differ only by the addition of cylindrical masses as shown in the figure. The radius of each additional mass is 1/4 the radius of the disc. Each cylinder and disc have equal mass. The ratio of time periods of the two torsion pendula is p. Then $27 p^{2}$ is.

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answer is 8.

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Detailed Solution

$\frac{T_{1}}{T_{2}} = \sqrt{\frac{I_{1}}{I_{2}}} \frac{T_{1}}{T_{2}} = \sqrt{\frac{M R^{2}}{\frac{227 M R^{2}}{16}}} \frac{T_{1}}{T_{2}} = P = \sqrt{\frac{8}{27}}$

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