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: a body of mass 10 kg 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

To find the least force required to pull the body up the plane.

Solution:

From figure,

The net force required

$F-f=mg\sin \theta ⟹F=mg\sin \theta +f⟹F=mg\sin \theta +\mu mg\cos \theta ⟹F=10\times 10\times \sin {30}^{\circ }+\frac{1}{2}\times 10\times 10\times \cos {30}^{\circ }⟹F=91.4N$

is the least force required to pull the body up the plane