Question

Two steel balls A and B of mass 10 kg and 10 g rolls towards each other with 5 m/s and 1 m/s respectively
on a smooth floor. After collision; with what speed B moves [perfectly elastic collision)?​

Answer 1

Answer:

lets name ball A be ball 1 with mass 'm₁' = 10kg , with

initial velocity 'u₁' = 5m/s & final velocity 'v₁' = ?

ball B be ball 2 with 'm₂' = 10g , with initial velocity 'u₂' = -1m/s

& final velocity 'v₂' = ?

observe that m₁ >> m₂ (we can ignore mass m₂ when comparing with m₁)

$v_2 = (\frac{2m_1}{m_1+m_2})*u_1 + (\frac{m_2-m_1}{m_1+m_2})*u_2$

Ignoring m₂ with respect to m₁

we have

$v_2 = (\frac{2m_1}{m_1})*u_1 + (\frac{-m_1}{m_1})*u_2$

$v_2 = 2*u_1 - u_2$

v₂ = 2(5m/s) - (-1m/s) = 11m/s

v₂ = 11m/s , the speed with which B bounces back.