Question

An object of mass $m$ is released from rest from the top of a smooth inclined plane of height $h$. Its speed at the bottom of the plane is proportional to:

• A. $m^0$
• B. $m$
• C. $m^2$
• D. $m^{-1}$

Answer 1

Answer: (A)

$m^0$

Let $v$ be the speed of the object at the bottom of the plane.
According to work-energy theorem
$W=△K=K_f-K_i$
$mgh=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2(\therefore u=0)$
$mgh=\frac{1}{2}m{v}^2$ or $v=\sqrt{2gh}$
From this expression, it is clear that $v$ is independent of the mass of an object.