Question

A body of mass 4 kg is moving with a velocity of 4 ms⁻¹. Find the ratio of its initial and final kinetic energy, if its mass is doubled and velocity is tripled.

Answer 1

Initial KE \[= \frac{1}{2}\, mv^{2} \]

\[= \frac{1}{2}\, (4\ \mathrm{kg})\, (4\ \mathrm{m\,s^{-1}})^{2}\]

= 32 J

Final KE \[ = \frac{1}{2}\, [2 \times 4\ \mathrm{kg}]\, [3 \times 4\ \mathrm{m\,s^{-1}}]^{2} \]

= 576 J

∴ Ratio of Initial KE and Final KE = 32 : 576 = 1 : 18.