Question

Two bodies A and B having masses in the ratio of 3 : 1 posses the same kinetic energy. The ratio of linear

momentum of B to A is

(A) 1 : 3 (B) 3 : 1 (C) 1: 3 (D) 3 :1

Answer 1

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Answer 2

Explanation:

Let m₁ and m₂ are masses of two bodies A and B respectively such that,

$\dfrac{m_1}{m_2}=\dfrac{3}{1}$

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

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

Since, the kinetic energies of both bodies are same. So,

$(\dfrac{p_1}{p_2})^2=\dfrac{m_1}{m_2}$

p₁ and p₂ are linear momentum of bodies A and B.

$(\dfrac{p_1}{p_2})^2=\dfrac{3}{1}$

$\dfrac{p_2}{p_1}=\dfrac{1}{\sqrt{3}}$

So, the ratio of linear  momentum of B to A is $\dfrac{1}{\sqrt{3}}$. Hence, this is the required solution.