A triangular block of mass `m` rests on a fixed rough inclined plane having friction coefficient `mu` with the block. A horizontal forces `F` is applied to it as shown in figure below, then the correct statements is:

Options

A. Friction force is zero when `F cos theta= mg sin theta`
B. The value of limiting friction is `mu(mg sin theta+ F cos theta)`
C. Normal reaction on the block is `F sin theta + mg cos theta`
D. The value of limiting friction is `mu ( mg sin theta-F cos theta)`

Answer

A, C

Explanation

`N=mg cos theta + F sin theta`
Also if `mg sin theta=F cos theta` then the friction force acting on the block is zero.
`f_("static")]_("maximum")=muN=mu(mg cos theta+Fsin theta)`
(The maximum static friction that can act on a body under a given solutions is known as limiting friction under the given conditions.)