Question

A block of mass m rests on a rough horizontal
surface as shown in the figure. Coefficient of
friction between the block and the surface is .
A force F = mg acting at angle with the vertical
side of the block pulls it. In which of the following
cases can the block be pulled along the surface?​

Answer 1

Answer:

cot theta/2≤u

Explanation:

from f.b.d

N=mg-mg cos theta

and

fs=mg sin theta

if the body is at rest so the friction is static.

fs≤uN

fs≤u(mg-mg cos theta)

mg sin theta≤umg(1-cos theta)

sin theta≤u(1- cos theta)

sin theta≤u(2 sin² theta/2)

2 sin theta/2 *cos theta/2≤u(2 sin² theta/2)

cot theta/2≤u