Question

In the figure shown, what force $‘F^{\prime }$ should be applied perpendicular to the plane on the block for it to not move. Given that the coefficient of static friction between the plane and the block is $0.5$.
(Assume limiting case of friction and take $g=10{\text{m/s}}^2$)

• A. $10\sqrt{2}\text{N}$
• B. $20\sqrt{2}\text{N}$
• C. $\frac{30}{\sqrt{2}}\text{N}$
• D. $\frac{10}{\sqrt{2}}\text{N}$

Answer 1

The correct option is A $10\sqrt{2}\text{N}$

FBD is given as


As system is in rest,

Perpendicular to the plane:
$N=(F+10\sqrt{2})\text{N}$

Along the plane
$20\sin {45}^{\circ }=f$
$10\sqrt{2}=\mu N=\mu (F+10\sqrt{2})$
$\Rightarrow 20\sqrt{2}=F+10\sqrt{2}$
$\Rightarrow F=10\sqrt{2}\text{N}$