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  • Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is (a) simple harmonic motion

Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
(a) simple harmonic motion
(b) non-periodic motion
(c) periodic motion
(d) periodic but not SHM

Answers (1)

The answer is the option (a) Simple harmonic motion and (b) non - periodic motion

Explanation: Lift the ball from point A to B and smoothly release it to reach C & then return to first A and then B. Thus, it is periodic motion. Here, mg sin ? balances the restoring force (R), also, a restoring force (mg \sin \theta)acts on the ball.

Thus, ma = mg \sin \theta

a = g \sin \theta or \frac{d^{2}x}{dt^{2} }= - g \sin \theta ….. (when the ball moves upward)

\frac{d^{2}x}{dt^{2} }= - g \left ( \frac{x}{r} \right )

Thus, \frac{d^{2}x}{dt^{2} }\propto (-x)

Thus, it is a simple harmonic motion.

\Omega =\sqrt{\frac{ g}{r}}   or T = \frac{2\pi }{\omega} = 2\pi \sqrt{\frac{r}{g}}

Thus, this motion is periodic as well as simple harmonic.

Posted by

infoexpert24

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