Question

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

• A. The velocity should be doubled
• B. The velocity should be halved
• C. The velocity should become four times
• D. The velocity should become one fourth

Answer 1

The correct option is B The velocity should be halved

Initial mass, $m_1=m$, initial velocity$=v_1$

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

So, for kinetic energy to remain constant,

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

or, $\frac{1}{2}m{v}_1^2=\frac{1}{2}\times 4m\times v_2^2$

or, $v_2^2=\frac{1}{4}{v}_1^2$

or, $v_2=\frac{1}{2}{v}_1$