First slide

Simple harmonic motion

Question

A solid sphere of mass 6 kg and radius 20 cm is suspended from a wire. The time period of its angular oscillation if the torque constant of the wire is $2 \times 10^{- 3} N m / r a d$ is

Easy

A

12.56 s
B

97.29s
C

15.32 s
D

22.89 s

Solution

$\begin{array}{l} For torsional pendulam, T = 2 π \sqrt{\frac{I}{c}} = 2 π \sqrt{\frac{2 M R^{2}}{5 c}} \\ T = 2 π \sqrt{\frac{2 \times 6 \times (0.2)^{2}}{2 \times 10^{- 3}}} \\ T = 4 π (\sqrt{\frac{6 \times 10^{- 2 + 3}}{1}}) \\ T = 4 π (7.74) = 97.29 s \end{array}$

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