Question

Three masses of $3\text{kg},4\text{kg}$ and $5\text{kg}$ respectively are having same kinetic energy. Which of these masses will move fastest?

• A. $3\text{kg}$
• B. $4\text{kg}$
• C. $5\text{kg}$
• D. All of these masses will have same speed

Answer 1

The correct option is A $3\text{kg}$

All three masses having same kinetic energy
$\because K.E_1=K.E_2=K.E_3$

Also we know that kinetic energy is given by, $KE=\frac{1}{2}m{v}^2$, where $m$ is mass of the body and $v$ is veocity of the body.

So, $m_1{v}_1^2=m_2{v}_2^2=m_3{v}_3^2$

It is given that, $m_1<m_2<m_3$
$\therefore v_1>v_2>v_3$
Mass of $3\text{kg}$ will move fastest among three masses.

Hence option A is the correct answer.

Alternate solution:

Given that kinetic energy of masses is equal,
so $KE=\frac{1}{2}m{v}^2=\text{Constant}$
so $v^2\propto \frac{1}{m}$
$v\propto \frac{1}{\sqrt{m}}$
If mass is least, velocity is highest.
Mass of $3\text{kg}$ will move fastest among three masses.

Hence option A is the correct answer.