Question

Two masses of 1 gm and of 4 gm are moving with equal linear momenta, the ratio of their kinetic energies is :

• A. 4:1
• B. $\sqrt{2}:1$
• C. 1:2
• D. 1:16

Answer 1

The correct option is A 4:1

Let masses are $m_1=1$ & $m_2=4$

If linerar momentum is equal $m_1{v}_1=m_2{v}_2$

So $\frac{v_1}{v_2}=\frac{m_2}{m_1}=\frac{4}{1}$

So ratio of kinetic energy is given by $\frac{\frac{1}{2}{m}_1{v}_1^2}{\frac{1}{2}{m}_2{v}_2^2}=\frac{{1.4}^2}{{4.1}^2}=\frac{4}{1}$

So the best possible answer is option A.