Question

If a ball of mass $4kg$ moving with velocity of $3m/s$ collides elastically head on with another ball of mass $6kg$ which is at rest, then the ratio of speed of second ball to first after collision will be

• A. 4 : 1
• B. 2 : 1
• C. 2 : 3
• D. 4 : 3

Answer 1

Answer: (A)

By conservation of linear momentum
$4\times 3=4v_1+6v_2$
$6=2v_1+3v_2...(i)$
$e=\frac{v_2-v_1}{3}=1$
$v_2-v_1=3$
$2v_2-2v_1=6...(ii)$
By solving equation (i) $\&$ (ii)
$v_2=\frac{12}{5}m{s}^{-1}$
$v_1=\frac{12}{5}-3$
$v_1=\frac{-3}{5}m{s}^{-1}$
$\frac{v_2}{v_1}=\frac{\frac{12}{5}}{\frac{3}{5}}$
$\frac{v_2}{v_1}=4:1$