Question

A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table. If the sphere is displaced from its equilibrium position and left, then executes SHM. The period of oscillation will be:

• A. $2\pi \sqrt{\frac{(R-r)1.4}{g}}$
• B. $2\pi \sqrt{\frac{(R-r)}{g}}$
• C. $2\pi \sqrt{\frac{\left(rR\right)1.4}{g}}$
• D. $2\pi \sqrt{\frac{R}{g}}$

Answer 1

The correct option is B $2\pi \sqrt{\frac{(R-r)}{g}}$

Tangential acceleration, $a_t=-g\sin \theta =-g\theta$

$a_t=-g\frac{x}{(R-r)}$

Motion is SHM., with time period

$T=2\pi \sqrt{\frac{displacement}{acceleration}}=2\pi \sqrt{\frac{x}{\frac{gx}{(R-r)}}}=2\pi \sqrt{\frac{R-r}{g}}$