Question

A particle A suffers an oblique elastic collision with a particle B, that is at rest initially. If their masses are the same, then, after collision

• A. they will move in opposite directions.
• B. A continues to move in the original direction while B remains at rest.
• C. they will move in mutually perpendicular directions.
• D. A comes to rest and B starts moving in the direction of the original motion of A.

Answer 1

The correct option is C they will move in mutually perpendicular directions.

Writing momentum conservation principle :
$\overrightarrow{P^{}}=\overrightarrow{P_1}+\overrightarrow{P_2}$...(i)
$|P{|}^2=|P_1{|}^2+|P_2{|}^2+2P_1{P}_2\cos \theta$....(ii)
From Conservation of Energy
Kinetic energy initial = Kinetic energy final
$\frac{P^2}{2m}=\frac{{P_1}^2}{2m}+\frac{{P_2}^2}{2m}$....(iii)
$|P{|}^2={|P_1|}^2+{|P_2|}^2$....(iv)
comparing (ii) and (iv) the angle $\theta$ should be ${90}^{\circ }$
Hence, both the bodies will move at right angle after the collision, option C is correct.