A block of mass 15 kg is resting on a rough inclined plane as shown in figure. The block is tied by a horizontal string which has a tension of 50 N. The coefficient of friction between the surfaces of contact is:

The string is under tension, hence there is limiting friction between the block and the plane.

$\sum _{ }{\mathrm{F}}_{\mathrm{x}} = 0 \Rightarrow \mathrm{\mu N} + 50 \cos {45}^0 = 150 \sin {45}^0----\left(\mathrm{i}\right)$

$\sum _{ }{\mathrm{F}}_{\mathrm{y}} = 0 \Rightarrow \mathrm{N} = 50 \sin {45}^0+150 \cos {45}^0-----\left(\mathrm{ii}\right)$

Solving (i) and (ii), $\mathrm{\mu } = \frac{1}{2}$