Question

For the same kinetic energy of a body, what should be the change in its velocity if its mass is increased to four times its original value?

• A. Velocity should be doubled
• B. Velocity should be halved
• C. Velocity should be constant
• D. Velocity is independent

Answer 1

The correct option is B

Velocity should be halved

Let the initial mass $m_1=m$, velocity$=v_1$

Final mass $m_2=4m,velocity=v_2$

Since the kinetic energy is same in both cases,

$\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}{m}_2{v}_2^2$

$\Rightarrow \frac{1}{2}m{v}^2=\frac{1}{2}4m\times v_2^2$

$\Rightarrow v_2^2=\frac{1}{4}{v}^2$

$\Rightarrow v_2=\frac{1}{2}v$

So in order to make the kinetic energy constant, the velocity of the body should be halved if mass is increased by four times .