Question

A body released from rest slides along a frictionless track $AC$. Its speed at $C$ is

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

Answer 1

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

$\because$ Total mechanical energy is conserved
Initial K.E + Initial P.E = Final K.E + Final P.E
So, the sum of kinetic energy $\left(K{E}_A\right)$ and potential energy $\left(P{E}_A\right)$ at point $A$ will be equal to the sum of kinetic energy $\left(K{E}_C\right)$ and potential energy $\left(P{E}_C\right)$ at point $C$
$\Rightarrow K{E}_A+P{E}_A=K{E}_C+P{E}_C$
$\Rightarrow 0+mgh=\frac{1}{2}m{v}_C^2+0$ [$\because v_A=0$ So $K{E}_A=0$ and base of incline is taken as reference]
$\Rightarrow v_C=\sqrt{2gh}$
Velocity at point $C$ is $\sqrt{2gh}$.