Small sphere of mass m and radius r is kept on fixed inclined rough surface. Surface makes an angle with the horizontal. Initially centre of sphere is at a height h above the horizontal floor. Coefficient of friction between the sphere and surface is u. Sphere is released from the state of rest.

Assume friction is not sufficient to provided pure rolling. Acceleration of the sphere is

Options

A. `g sin theta- mu g cos theta`
B. `g sin theta`
C. `mug cos theta`
D. `(5)/(7) g sin theta- mug cos theta`

Answer

A

Explanation

We can refer to same figure in the previous part. When friction is not sufficient enough to support pure rolling then `a ne r alpha` and friction becomes maximum.
`f = muN = mu mg cos theta`
We can apply F = ma along the plane to get acceleration of sphere.
`mg sin theta - mu mg cos theta = ma`
`rArr a= g sin theta- mu g cos theta`