Question

A ball of mass 0.1kg makes an elastic head on collision with a ball of unknown mass,initially at rest .if the 0.1kg ball rebounded at one third of its original speed, what is the mass of the other ball?

Answer 1

for elastic collision between two balls we can say momentum of two balls is conserved

$P_{1i} + P_{2i} = P_{1f} + P_{2f}$

now we have

$m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$

$0.1*v_{1i} + m_2*0 = 0.1*(-\frac{v_{1i}}{3}) + m_2v_{2f}$

$\frac{0.4v_{1i}}{3} = m_2v_{2f}$

also for elastic collision we can say

$v_{2f} - v_{1f} = v_{1i} - v_{2i}$

$v_{2f} - (-\frac{v_{1i}}{3}) = v_{1i} - 0$

$v_{2f} = \frac{2v_{1i}}{3}$

now from above two equations

$\frac{0.4v_{1i}}{3} = m_2*  \frac{2v_{1i}}{3}$

$m_2 = 0.2 kg$

so mass of other ball is 0.2 kg

Answer 2

mass of ball two is 0.2kg