Two balls of clay of known masses hang from the ceiling on massless strings of equal length. They barely touch when both hang at rest. One ball is pulled back until its string is at $45°$, then released. It swings down, collides with the second ball, and they stick together. To determine the angle to which the balls swing on the opposite side, would you invoke

(a) conservation of momentum, (b) conservation of mechanical energy, (c) both, (d) either but not both, or (e) these laws alone are not sufficient to find the angle? Explain.

We need to find the angle to which the balls swing on the opposite side, after invoke

The two balls of clay are hung from the ceiling and initially do not touch each other.

One of the balls is pulled till and then it was left to swing. It collides with another ball and they stick together.

After determining the angle they will make on the opposite sides and get stuck together. For that, we will need the following principle.

(i)Conservation of momentum: In direction of swinging there is no external force hence their net momentum should be conserved. Using this we can find their common velocity.

(ii) Conservation of energy: By applying this we can determine the angle they make. We can break the gravity force in the required directions and use that to find the angle.

Hence the correct option is (c).