Question 19 of 130
A thin rod of mass and length is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move moving in a straight line with velocity hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in ) of the rod immediately after the collision will be …………
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Answer: 20
Given,
Mass of the rod,
Mass of particle,
Length of the rod,
Velocity of particle,
No external torque acting on the system of rod and particle, so angular momentum of system about the suspension is conserved, i.e.;
Where, is the momentum of inertia of rod and particle system, is the angular velocity of system just after the collision.
Substitute the values in equation (2)
Mass of the rod,
Mass of particle,
Length of the rod,
Velocity of particle,
No external torque acting on the system of rod and particle, so angular momentum of system about the suspension is conserved, i.e.;
Where, is the momentum of inertia of rod and particle system, is the angular velocity of system just after the collision.
Substitute the values in equation (2)
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