Question

A block od mass 20 kg is kept on rough incline plane. If angle of repose is ${30}^o$, Then what should be value of $F_{e}xt$ so that the block does not move over incline plane?

• A. 120 N
• B. 200 N
• C. 110 N
• D. Both (1) & (2)

Answer 1

The correct option is A 120 N

To keep the block at rest

$f_{min}=mg(\sin {60}^{\circ }=uk\cos {60}^{\circ })$

$=200\left(\frac{1}{2}\right)(\sqrt{3}-u)=100(\sqrt{3}-u)$

$\therefore$ force required to keep the block at rest is

$100(\sqrt{3}-u)$

$\mu =\frac{1}{\sqrt{3}}$

$f_{ent}=100(\sqrt{3}-\frac{1}{\sqrt{3}})$

$f_{ent}=100\left(\frac{1}{\sqrt{3}}\right)$

$f_{ent}=117.8N\approx 120$