Question

A body has a KE 'P'. If the mass of body increases 25 times, calculate its velocity, the kinetic energy remaining same.

Answer 1

Let initial velocity = v

\[ \therefore \text{KE} = \frac{1}{2}mv^{2} \qquad \text{.....(i)} \]

When mass increases 25 times, let velocity be v₁,

\[ \therefore \text{KE} = \frac{1}{2} \times 25\ mv_{1}^{2} \qquad \text{.....(ii)} \]

As KE remains the same,

\[ \therefore\ \frac{1}{2} \times 25\, m v_{1}^{2} = \frac{1}{2}\, m v^{2} \]

\[ 25\, v_{1}^{2} = v^{2} \]

Or \[v_{1} = \frac{v}{5}\]