Question

Assertion :STATEMENT-1 : In a perfectly inelastic collision between two spheres, velocity of both spheres just after the collision are not always equal. Reason: STATEMENT-2 : For two spheres undergoing collision, component of velocities of both spheres along line of impact just after the collision will be equal if the collision is perfectly inelastic. The component of velocity of each sphere perpendicular to line of impact remains unchanged due to the impact.

• A. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement-1 is True, Statement-2 is False
• D. Statement-1 is False, Statement-2 is True

Answer 1

The correct option is A Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

We know the relation that,

$velocityofseparation=eXvelocityofapproach$

where is the coefficient of restitution. In case of inelastic collision, $e=0$. Hence component of velocity along line of impact will be same as this is the component deciding the velocity of separation. The component of velocity perpendicular to the line of impact will remain unchanged since no forces act on either sphere along this direction.

Hence both the statements ate correct and R is correct explanation fro A.