Question

A body of mass $10kg$ is on a rough inclined plane having an inclination of ${30}^o$ with the horizontal. If coefficient of friction between the surfaces of contact of the body and the plane is $0.5$. Find the least force required to pull the body up the plane.

• A. $80.5N$
• B. $91.4N$
• C. $85.4N$
• D. $78.4N$

Answer 1

The correct option is B $91.4N$

Given that,

Mass $m=10kg$

Inclination angle $\alpha ={30}^0$

Friction coefficient $\mu =0.5$

Normal reaction, $N=mg\cos \alpha$

Friction force,$F_f=\mu N=\mu mg\cos \alpha$

Net pulling force, $F=F_r+mg\sin \alpha$

$F=\mu mg\cos {30}^o+mg\sin {30}^o$

$F=0.5\times 10\times 9.8\times \frac{\sqrt{3}}{2}+10\times 9.8\times \frac{1}{2}=91.4N$

Hence, the pulling force is $91.4N$