Question

Two bodies of mass m and 4m have equal kinetic energy. What is the ratio of their momentum

Answer 1

Answer:

1:1

Explanation:

let, bodies are A and B

Given

K.E.(A) = K.E.(B)

To Find:

Ratio of their momentum

Solution:

$\boxed{K.E.= \dfrac{1}{2} m{v}^{2}}$

$\dfrac{1}{2} m {v_1}^{2} = \dfrac{1}{2} (4m) {v_2}^{2}$

${v_1}^{2} = 4{v_2}^{2}$

$\dfrac{ {v_1}^{2}} {{v_2}^{2}} = 4$

$\dfrac{ v_1} {v_2} = 4$

Now,,

$\boxed{P= mv}$

$\dfrac{ P_1} {P_2} = \dfrac{ mv_1} {4mv_2}$

$\dfrac{ P_1} {P_2} = \dfrac{ 4} {4}$

$\dfrac{ P_1} {P_2} = \dfrac{ 1} {1}$