Question

What happens to the kinetic energy when mass of body is doubled, but velocity is reduced to half?

Answer 1

The kinetic energy is halved (becomes \(\frac{1}{2}\) times).

Mathematical Derivation:

Original Kinetic Energy:

\[ K = \frac{1}{2}mv^{2} \]

Substituting new mass \(m' = 2m\) and new velocity \[ v' = \frac{v}{2} \]:

\[ K' = \frac{1}{2}(2m)\left(\frac{v}{2}\right)^{2} \]

\[ = m\left(\frac{v^{2}}{4}\right) \]

\[ = \frac{1}{2} \times \left(\frac{1}{2}mv^{2}\right) \]

\[ = {\frac{1}{2}\,K} \]