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  • A sphere of radius is kept on a concave mirror of radius of curvature <img alt="2 R" src="https://entrancecorner.oncodecogs.c

A sphere of radius r is kept on a concave mirror of radius of curvature 2 R. The arrangement is kept on a horizontal table (the surface of the concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be?

Option: 1

2 \pi \sqrt{\frac{2 R-r}{g}}.


Option: 2

\pi \sqrt{\frac{2 R-r}{g}}.


Option: 3

3 \pi \sqrt{\frac{2 R-r}{g}}.


Option: 4

4 \pi \sqrt{\frac{2 R-r}{g}}.


Answers (1)

best_answer

Tangential acceleration, \mathrm{a}_{\mathrm{t}}=-\mathrm{g} \sin \theta=-\mathrm{g} \theta

a_t=-g \frac{x}{2 R-r}

Motion is SHM, with time period

T=2 \pi \sqrt{\frac{\text { displacement }}{\text { acceleration }}}=2 \pi \sqrt{\frac{x}{\frac{g x}{2 R-r}}}=2 \pi \sqrt{\frac{2 R-r}{g}}

In this case, the period of oscillation for the sphere on the concave mirror with a radius of

curvature 2R is  2 \pi \sqrt{\frac{2 R-r}{g}}

Posted by

manish painkra

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