Question

In the given figure, a ball strikes a rod (hinged at point $A$) elastically. The rod is free to rotate in the vertical plane. Then, identify the correct statement.

• A. Linear momentum of system of (ball + rod) is conserved.
• B. Angular momentum of system of (ball+ rod) about hinged point $A$ is conserved.
• C. Initial kinetic energy of the system is equal to final kinetic energy of the system.
• D. Linear momentum of ball is conserved.

Answer 1

The correct option is B Angular momentum of system of (ball+ rod) about hinged point $A$ is conserved.

During elastic collision, only total mechanical energy of a system will be conserved.
On the system of (rod+ball), $F_{\text{ext}}\ne 0$ as hinge force has a component along $x\&y$ direction.
$\therefore$ Linear momentum will not be conserved.


Since, $F_x\&F_y$ and $mg\left(\text{(weight of system)}\right)$ pass through $A$ and , net ${\tau }_{\text{ext}}=0$ About the hinged point $A$.
$\Rightarrow$Angular momentum of (ball+rod) remains conserved about point $A$.

$\because$ On the ball, impulse $\left(J\right)$ from the rod acts as shown in figure, hence it will cause change in the linear momentum of the ball.


So, linear momentum of the ball will not be conserved.
Only option (B) is correct.