A disc of mass m is connected with an ideal spring of spring constant k inside a lift as shown. The left starts moving with constant acceleration `(a hat (i)- a hat (j))`. At the same moment disc starts rolling without sliding on the wall of lift (from rest). If spring is in natural length initially then friction force acting on disc as a function of y is given by : (y is the displacement of the disc with respect to lift)

Options

A. (A) `-ky`
B. (B) `(2)/(3)(mg + ma-ky)`
C. (C) `(1)/(3) (mg +ma-ky)`
D. (D) `mg+ma-2ky`

Answer

C

Explanation

`((mg + ma - ky)R)/((3)/(2)mR^(2)) = (frR)/((1)/(2)mR^(2))`
`rArr fr = (1)/(3) (mg + ma - ky)`