Question

The ratio of the magnitude of linear momentum for two objects having mass 30 kg and 10 kg respectively with equal kinetic energy is

1. \(\sqrt {\frac{1}{3}}\)
2. (3)2
3. √3
4. \(\left( {\frac{1}{\sqrt 3}}\right)^2\)

Answer 1

Correct Answer - Option 3 : √3

Concept:

Linear momentum of a body is given as P = m x V

The kinetic energy of the body is given as \(K.E. = \frac {1}{2} mv^2\)

m = mass of the body, v = velocity of the body

Calculation:

Given:

mass m₁ = 30 kg, m₂ = 10 kg

Let the velocity of respective body 1 and 2 = v₁, v₂

The kinetic energy of body 1 and 2 is equal, KE₁ = KE₂

\( \frac {1}{2} m_1v_1^2= \frac {1}{2} m_2v_2^2\)

\( \frac {1}{2} (30) v_1^2 = \frac {1}{2} (10)v_2^2\) ⇒ \(\frac {v_1}{v_2} = \frac {1}{\sqrt3}\)  

\(\frac {P_1} {P_2} = \frac {m_1v_1}{m_2v_2} = \frac {30}{10}\times \frac {1}{\sqrt3}\)

\(\frac {P_1} {P_2} = \frac {3}{1}\times \frac {1}{\sqrt3} = \frac {\sqrt 3}{1} = \sqrt3\)