Question

A block of mass 2 kg is kept on a smooth wedge of mass 3 kg and wedge is kept on a rough horizontal surface as shown in the figure. A vertical force of 60 N is applied on the block as shown in the figure. What should be the minimum coefficient of friction between the wedge and horizontal surface so that wedge remains at rest during the motion of the block on the wedge?

• A. 2/7
• B. 4/7
• C. 6/7
• D. 2/5

Answer 1

The correct option is B 4/7

$f_3=N_{1}sin{45}^{\circ }\le {\mu }_s{N}_2$

$⟹\frac{N_1}{2}={\mu }_3[3g+\frac{N_1}{\sqrt{2}}]$

$⟹\frac{N_1}{3\sqrt{2}g+N_1}\le {\mu }_s$

$N_1=\frac{8g}{\sqrt{2}}=4\sqrt{2}g$

Putting the value of $N_1$ we get, ${\mu }_s\ge \frac{4}{7}$