Oscillations - Result Question 33
36. The angular velocity and the amplitude of a simple pendulum is $\omega$ and a respectively. At a displacement $x$ from the mean position if its kinetic energy is $T$ and potential energy is $V$, then the ratio of $T$ to $V$ is
[1991]
(a) $\frac{(a^{2}-x^{2} \omega^{2})}{x^{2} \omega^{2}}$
(b) $\frac{x^{2} \omega^{2}}{(a^{2}-x^{2} \omega^{2})}$
(c) $\frac{(a^{2}-x^{2})}{x^{2}}$
(d) $\frac{x^{2}}{(a^{2}-x^{2})}$
Topic 3: Time Period, Frequency, Simple
Pendulum & Spring Pendulum37. A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt
[NEET Odisha 2019]
(a) to the left and angle of inclination of the pendulum with the vertical is $\tan ^{-1}(\frac{g}{a})$
(b) to the left and angle of inclination of the pendulum with the vertical is $\sin ^{-1}(\frac{g}{a})$
(c) to the left and angle of inclination of the pendulum with the vertical is $\tan ^{-1}(\frac{a}{g})$
(d) to the left and angle of inclination of the pendulum with the vertical is $\sin ^{-1}(\frac{a}{g})$
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Answer:
Correct Answer: 36. (c)
Solution:
- (c) P.E., $V=\frac{1}{2} m \omega^{2} x^{2}$
and K.E., $T=\frac{1}{2} m \omega^{2}(a^{2}-x^{2})$
$\therefore \frac{T}{V}=\frac{a^{2}-x^{2}}{x^{2}}$
