Question

A block of mass m slides along a frictionless surface as shown in the figure. If it released from rest at A, what is its speed at B?

• A. v = gh
• B. v = 2gh
• C.
• D.

Answer 1

The correct option is C

Take the block + the earth as the system. Only the block moves, so only the work done on the block will contribute to the gravitational potential energy. As it descends through a height h between A and B, the potential energy decreases by mgh. The normal contact force N on the block by the surface does no work as it is perpendicular to its velocity. No external force does any work on the system. Hence,

Increase in kinetic energy = decrease in potential energy or, $\frac{1}{2}m{v}^2=mgh$ or , $v=\sqrt{2gh}$