Question

Two masses 1 kg and 4 kg are moving with equal kinetic energies. The ratio of magnitudes of their linear momentum is

• A. 1:2
• B. 1:4
• C. 2:1
• D. 4:1

Answer 1

The correct option is A 1:2

Let the velocity be $v_{1}and{v}_2$

$K.E_1=\frac{m{v}^2}{2}=\frac{1\times v_1^2}{2}$

$K.E_2=\frac{m{v}^2}{2}=\frac{4\times v_2^2}{2}$

now $K.E_1=K.E_2$

so we get $v_1=2v_2$

now ratio of momentum ratio ,$n=\frac{1\times v_1}{4\times v_2}=\frac{2v_2}{4v_2}$

so $n=\frac{1}{2}$