Question

A trolley-car starts from rest at the top of a hill as shown in the figure and moves down the curved track. Determine its speed as it reaches the bottom. Assume that the work done by frictional forces is negligible.

• A. $\sqrt{gh}$
• B. $\sqrt{2gh}$
• C. $\sqrt{3gh}$
• D. $\sqrt{4gh}$

Answer 1

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

As the trolley-car moves along the curved track, the only force acting on it is the force of gravity in the downward direction.

Assuming the velocity of the trolley car at the bottom of the hill is $v$.


Figure shows the complete description of the problem only one conservative force is working on the block. So from mechanical energy conservation

$K{E}_f+P{E}_f=K{E}_i+P{E}_i$

$\frac{1}{2}m{v}^2+0=0+mgh$

$v=\sqrt{2gh}\text{m/sec}$

Hence, option $\left(b\right)$ is correct.

Why this question? Let $(W.D{)}_{N.C}=$ work done by non-conservative force. $(W.D{)}_{ext}=$ work done by external force $(W.D{)}_{pseudo}=$ work done by pseudo force. If $(W.D{)}_{N.C}=(W.D{)}_{ext}=(W.D{)}_{pseudo}=0$ $K_f+U_f=K_i+U_i$ This is called mechanical energy conservation law.