A sphere of catius r is kept on a concave of mirror radius of curation `R`. The arrangement a kept on a horizontal tavke (the surface of concave mirror is fricationless 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

Options

A. `2 pi sqrt((((R - r)1.4)/(4)))`
B. `2 pi sqrt(((R - r)/(g)))`
C. `2 pi sqrt(((rR)/(a)))`
D. `2 pi sqrt(((R)/(gr)))`

Answer

B

Explanation

Tengental acceleration, `a_(1) = - g sin theta = -g theta`
`a_(1) = - g'(x)/((R - r))`

Motion is `S.H.M.` is with time period
`T = 2pi sqrt(("displacement")/("acceleration")) = 2 pisqrt((x)/((gx)/((R - r)))) = 2pi sqrt((R - r)/(g))`