Question

Two bodies of mass 3 kg and 1 kg have equal momentum. Ratio of their kinetic energy is:

• A. 1:1
• B. 9:1
• C. 2:1
• D. 1:3

Answer 1

The correct option is D

1:3

Let velocity of 3 kg and 1kg be $v_1$ and $v_2$ respectively
Now, momentum of 3 kg = Momentum of 1 kg(Given)
We know that momentum of a body = mass $\times$ velocity

|(\therefore\)$\Rightarrow 3\times v_1=1\times v_2$

$\Rightarrow \frac{v_1}{v_2}=\frac{1}{3}$
Let their kinetic energies be $K.E_1$ and $K.E_2$ respectively.

$\frac{K.E_1}{K.E_2}=\frac{\frac{1}{2}\times 3\times v_1^2}{\frac{1}{2}\times 1\times v_2^2}=3\times (\frac{v_1}{v_2}{)}^2=3\times (\frac{1}{3}{)}^2=\frac{1}{3}$