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 S.H.M.

This is a multiple choice answer as classified in NCERT Exemplar

(a), (c) consider the motion of a ball inside a smooth curved bowl

for small angular displacement or slightly released motion, it can be considered as angular SHM.

When the ball is at angle $\theta$ of  the restoring force acts

Ma=mgsin $\theta$

A= gsin $\theta$

$\frac{d^{2}x}{{dt}^2}=-gsin\theta =-g\frac{x}{R}$

Hence motion is SHM

So T=   $\frac{2\pi }{w}=2\pi \sqrt[]{\frac{R}{g}}$

<div><div><div><div><p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p> (a), (c) consider the motion of a ball inside a smooth curved bowl</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745494548phplpVVeq_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745494548phplpVVeq.jpeg" alt="" width="162" height="145"></picture></div><div><p>for small angular displacement or slightly released motion, it can be considered as angular SHM.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745494592phpJ25TId_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745494592phpJ25TId.jpeg" alt="" width="181" height="149"></picture></div><div><p>When the ball is at angle<span contenteditable="false"> <math> <mi>θ</mi> </math> </span> of &nbsp;the restoring force acts</p><p>Ma=mgsin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span></p><p>A= gsin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span></p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mi>g</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>θ</mi> <mo>=</mo> <mo>-</mo> <mi>g</mi> <mfrac> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>Hence motion is SHM</p><p>So T= <strong>&nbsp;<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mi>g</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></strong></p></div></div></div></div></div></div></div></div>

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