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
\( \frac {1}{2} m_1v_1^2= \frac {1}{2} m_2v_2^2\)
\( \frac {1}{2} (30) v_1^2 = \frac {1}{2} (10)v_2^2\) ⇒ \(\frac {v_1}{v_2} = \frac {1}{\sqrt3}\)
\(\frac {P_1} {P_2} = \frac {m_1v_1}{m_2v_2} = \frac {30}{10}\times \frac {1}{\sqrt3}\)
\(\frac {P_1} {P_2} = \frac {3}{1}\times \frac {1}{\sqrt3} = \frac {\sqrt 3}{1} = \sqrt3\)