Question

Momentum of two bodies are equal. If the mass
of bodies are mı, m2 and kinetic energies are
k2
ki, k2 respectively, then the ratio k2/k1 would be?​

Answer 1

Answer: The kinetic energies of the two bodies are in the inverse ratio of their masses.

Explanation:

Formula for momentum is given by the formula,

momentum = p = mass X velocity

$m_1v_1$ = $m_2v_2$ = p = Since both the bodies have equal momentum

For Body 1,

$v_1$ = $\frac{p}{m1}$ ............equation 1

Similarly for  body 2,

$v_{2}$ = $\frac{p}{m2}$   ..............equation 2

Kinetic energy of body =  $\frac{1m}{2V^2}$

Kinetic energy of body 1,  $k_{1}$ = $\frac{1m_1}{2V_1^2}$

Kinetic energy of body 2,  $k_{2}$ = $\frac{1m_2}{2V_2^2}$

Substituting the values of $v_1$  & $v_{2}$  from equation 1 & 2,

$k_{1}$ = $\frac{p^2}{2m_1}$

$k_{2}$ = $\frac{p^2}{2m_2}$

∴ Ratio of $k_{2}$ to $k_{1}$  = ($\frac{p^2}{2m_2}$) / $\frac{p^2}{2m_1}$

$\frac{k_2}{k_1}$ = $\frac{m_1}{m_2}$