Question

Two bodies of masses m and 4m are moving with equal kinetic energies. The ratio of their linear momenta is

• A. $1 : 2$
• B. $1 : 4$
• C. $4 : 1$
• D. $1 : 1$

Answer 1

Answer: (A)

$1 : 2$

Answer 2

Mass of first body = m;

Mass of second body = 4m and KE$_1$ = KE$_2$.

Linear momentum of a body

p=$\sqrt{2mE} \sqrt m .$

Therefore $\frac{p_1}{p_2}=\sqrt{\frac{m_1}{m_2}}=\sqrt{\frac{m}{4m}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

or $p_1:p_2 = 1: 2.$