Explanation
As the inclined plane is frictionless therefore all the bodies will slide down along the inclined plane with same acceleration g sin θ
Initially both the particles are at rest, so velocity of centre of mass is equal to zero and no external force acts on the system, therefore its velocity of centre of mass remains constant i.e., zero.
Force does not produce any torque because it passes through the centre (Point of rotation) and we know that if τ = 0 then L = constant.
As the shell is initially at rest and after explosion, according to law of conservation of linear momentum, the centre of mass remains at rest. While parts of shell move in all direction, such that total momentum of all parts is equal to zero.
When beads slides down then moment of inertia of the system increases and accordingly angular velocity decreases. But angular momentum of the system remains conserved because external torque on the system is zero. Also total energy of system remains conserved because there is no dissipative force.
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