Question

A body of mass $200g$ begins to fall from a height where its potential energy is $80J$. Its velocity at a point where kinetic and potential energies are equal is:

• A. $4m/s$
• B. $400m/s$
• C. $20m/s$
• D. $10\sqrt{8}m/s$

Answer 1

The correct option is C $20m/s$

Mass of the body $m=200g$ $=0.2kg$

According to conservation of energy, the sum of potential energy and kinetic energy is constant at every instant and is equal to total energy of the system.

$\therefore$ $K.E+P.E=80J$

$⟹$ $K.E+K.E=80J$

or, $K.E=40J$

Let the velocity of body be $v$ at the instant when its kinetic energy and potential energy are equal.

$\therefore$ $\frac{1}{2}m{v}^2=40$

or, $\frac{1}{2}\times 0.2v^2=40$ $⟹v^2=400$ or, $v=20$ $m/s$