Question

A particle of mass $m$ moving in the $x-$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y-$ direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

• A. 55.55
• B. 55
• C. 56
• D. 55.5
• E. 56.0
• F. 56.00

Answer 1

Answer: (A), (B), (C), (D), (E), (F)

From conservation of momentum,
$P_{xi}=P_{xf}$
$2mv=3m{v}_x$
$\Rightarrow v_x=\frac{2v}{3}$
$P_{yi}=P_{yf}$
$2mv=3m{v}_y$
$\Rightarrow v_y=\frac{2v}{3}$

Final kinetic energy of system
$K{E}_f=\frac{1}{2}3m(v_x^2+v_y^2)=\frac{1}{2}3m[\frac{4v^2}{9}+\frac{4v^2}{9}]$
$K{E}_f=\frac{4m{v}^2}{3}$

Initial kinetic energy of system
$K{E}_i=\frac{1}{2}m(2v{)}^2+\frac{1}{2}2m(v^2)=2m{v}^2+m{v}^2=3m{v}^2$
$\%\text{Loss}=\frac{K{E}_i-K{E}_f}{K{E}_i}=100=\frac{3m{v}^2-\frac{4m{v}^2}{3}}{3m{v}^2}\times 100$
$=\frac{5}{9}\times 100=55.5\%\approx 56\%$
The correct option is (B)