Question

A body of mass 'm' starts from rest and slides down an inclined plane of height h, and angle $\theta$. The velocity of the body when it reaches the bottom if the incline is smooth is-

• A. $\sqrt{2gh}$
• B. $2gh$
• C. $2\sqrt{2}gh$
• D. $\frac{1}{\sqrt{2}gh}$

Answer 1

The correct option is A $\sqrt{2gh}$

Word one by the forces N and, which are normal to the surface, is zero.

Work done by the force mg sin $\theta$ = (mg sin $\theta$) AB,

= $\frac{mgsin\theta \times h}{sin\theta }$,

= mgh.

[Note : This the same work done by gravity on the body if the body is displaced through BC].

Work = change in kinetic energy

mgh = $\frac{1}{2}m{v}^2\Rightarrow v=\sqrt{2gh}$