First slide

Simple harmonic motion

Question

An sphere of moment of inertia 4 kg/m² passing through the diameter. It is suspended from a steel wire of negligible mass, whose couple per unit twist is 81 Nm/rad. It is allowed to execute small angular oscillations. The angular frequency of oscillation is

Easy

A

$\frac{9}{2} r a d / s$
B

$\frac{9}{4} r a d / s$
C

$\frac{9}{2 π} r a d / s$
D

$\frac{9}{4 π} r a d / s$

Solution

For torsional pendulum, $T = 2 π \sqrt{\frac{I}{c}}$ Hence angular frequency of oscillation is
$\begin{array}{l} ω = \sqrt{\frac{c}{I}} \\ ω = \sqrt{\frac{81}{4}} \\ ω = \frac{9}{2} \\ ω = 4.5 rad / s \end{array}$

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