Question

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

(1) 1 : 3 

(2) 3 : 1 

(3) 1 : √3

(4) √3 : 1

Answer 1

Correct option is (3) 1 : √3

\(P = \sqrt {2mE}\)

\(\therefore \frac {P_1}{P_2} = \sqrt {\frac {m_1}{m_2}}\) (if E = constant)

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

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