Question

(a) Find the time period of oscillations of a torsional pendulum,if the torsional constant of the wire is $K=10{\pi }^{2}J/rad$.The moment of inertia of rigid body is $10kg{m}^2$ about the axis of rotation.
(b) A simple pendulum of length l=0.5 m is hanging from ceiling of a car. The car is kept on a horizontal plane.The car starts accelerating on the horizontal road with acceleration of $5m/s^2$.Find the time period of oscillations of the pendulum for small amplitudes about the mean position

• A. (a) 2sec, (b) $T=0.628sec$
• B. (a) 3sec, (b) $T=\frac{2}{5^{1/4}}sec$
• C. (a) 2sec, (b) $T=\frac{2}{5^{1/3}}sec$
• D. (a) 4sec, (b) $T=\frac{2}{5^{1/4}}sec$

Answer 1

The correct option is A (a) 2sec, (b) $T=0.628sec$

The time period of oscillation of torsional pendulum is given by
$T=2\pi \sqrt{\frac{I}{K}}$ where $I$ is the moment of inertia and $K$ is the torsional constant
$T=2\pi \sqrt{\frac{10}{10{\pi }^2}}=2s$
Time period of oscillation of simple pendulum is given by:
$T$ $=$ $2\pi \sqrt{\frac{L}{\sqrt{g^2+a^2}}}$
$T=2\pi \sqrt{\frac{0.5}{\sqrt{100+5^2}}}=\frac{2\pi }{10}sec$
$T=\frac{22}{35}=0.628sec$