Question

Which of the following bodies has the largest kinetic energy?

• A. Mass $3M$ and speed $V$
• B. Mass $3M$ and speed $2V$
• C. Mass $2M$ and speed $3V$
• D. Mass $M$ and speed $4V$

Answer 1

Answer: (C)

Mass $2M$ and speed $3V$

We know that, the kinetic energy is

$K.E=\frac{1}{2}m{v}^2....\left(I\right)$

Checking all options given -

A) $m=3M$ & $v=v$

$K.E=\frac{1}{2}m{v}^2$

$K.E=\frac{1}{2}\times 3M\times v^2$

$K.E=\frac{3M{v}^2}{2}$

B) $m=3M$ & $v=2v$

$K.E=\frac{1}{2}m{v}^2$

$K.E=\frac{1}{2}\times 3M\times 4v^2$

$K.E=6M{v}^2$

C) $m=2M$ & $v=3v$

$K.E=\frac{1}{2}m{v}^2$

$K.E=\frac{1}{2}\times 2M\times 9v^2$

$K.E=9M{v}^2$

D) $m=M$ & $v=4v$

$K.E=\frac{1}{2}\times M\times 16v^2$

$K.E=8M{v}^2$

Hence, the largest kinetic energy is $9M{v}^2$ when $m=2M$ and $v=3v$.