Question

find the ratio of kinetic energies of two bodies of masses 1 kg and 4 kg having equal linear momentum

Answer 1

this is your ans ....I hope it will help you....

Answer 2

Answer:

$\dfrac{E_1}{E_2}=\dfrac{4}{1}$

Explanation:

It is given that,

Mass of first body, m₁ = 1 kg

Mass of second body, m₂ = 4 kg

The relation between the kinetic energy and the linear momentum is given by :

$E=\dfrac{p^2}{2m}$

For body 1,

$E_1=\dfrac{p_1^2}{2m_1}$

For body 2,

$E_2=\dfrac{p_2^2}{2m_2}$

Since, $p_1=p_2$ (given)

$\dfrac{E_1}{E_2}=\dfrac{p_1^2m_2}{p_2^2m_1}$

$\dfrac{E_1}{E_2}=\dfrac{m_2}{m_1}$

$\dfrac{E_1}{E_2}=\dfrac{4}{1}$

So, the ratio of the kinetic energy of the two bodies is 4:1. Hence, this is the required solution.