Question

If two bodies of masses 3 gm and 5 gm moving with linear momenta in the 3:5, the ratio of their kinetic energies is

• A. 4 : 15
• B. 3 : 5
• C. 5 : 6
• D. 5:3

Answer 1

The correct option is D 5:3

Given that,

Mass $m_1=3g$

Mass $m_2=5g$

Now, masses is

$\frac{m_1}{m_2}=\frac{3}{5}$

Now, the momentum is

$P_1=m{v}_1$

$P_1=3v_1$

$P_2=m{v}_2$

$P_2=5v_2$

Now,

$p_1=p_2$

$3v_1=5v_2$

$\frac{v_1}{v_2}=\frac{5}{3}$

Now, the kinetic energy is of both bodies

$K.E=K.E$

$\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}{m}_2{v}_2^2$

$\frac{K.E_1}{K.E_2}=\frac{3}{5}\times \frac{25}{9}$

$\frac{K.E_1}{K.E_2}=\frac{5}{3}$

Hence, the ratio of kinetic energy is $5:3$