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

C, D

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 ") = mu N = mu (mg cos theta + F sin theta )`
(The maximum static friction that can act on a body under a given solution is known as limiting friction under the given conditions) .