Question

Which one of the following statements is true regarding collision of bodies in absence of external forces? (Considering all surfaces to be smooth)

• A. Momentum is conserved in collision but kinetic energy is conserved only in case of elastic collision.
• B. Momentum is conserved in collision but not kinetic energy.
• C. Both momentum and kinetic energy are conserved in all cases of collision.
• D. Neither momentum nor kinetic energy is conserved in elastic collision.

Answer 1

The correct option is A Momentum is conserved in collision but kinetic energy is conserved only in case of elastic collision.

From the statement of newton's $2^{\text{nd}}$ law of motion:
$\overrightarrow{F}=\frac{\overrightarrow{dP}}{dt}$
Where, $\overrightarrow{F}=\text{Net external force}$
$\therefore$When net external force is $\text{zero}$ in a particular direction, then linear momentum remains conserved along that direction.

$\Rightarrow$In case of collision, the forces exerted by body on each other becomes internal force, for the system of colliding objects, hence linear momentum is conserved if other external forces are absent.

$\Rightarrow$ No deformation occurs in case of elastic collision so, kinetic energy is conserved. In case of inelastic collision, some part of kinetic energy gets transformed to other forms of energy.