Question

A body slides down a smooth inclined plane of height $h$ and angle of inclination ${30}^0$ reaching the bottom with a velocity $v$. Without changing the height, if the angle of inclination is doubled, the velocity with which it reaches the bottom of the plane is

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

Answer 1

The correct option is A $v$

We know,
When a body slides down a smooth inclined plane,
According to Work energy theorem,
$mgh=\frac{1}{2}\times m{v}^2$
Thus the velocity with which it reaches the bottom of the plane is given by,
$V=\sqrt{2gh}$
and thus V does not depend on $\theta$ when h$=$constant
So, the velocity remains same even if the inclination changes so far h remains constant.