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## Homework Statement

A rod of mass ##M## and length ##l## is pivoted at the center(##O##) in horizontal position. An object of equal mass(having velocity ##v##) falls vertically on the rod at distance ##\frac{l}{4}## from ##O## and sticks to it. Find the angular velocity of the rod just after that object falls on the rod.

## Homework Equations

## The Attempt at a Solution

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I know this question can be solved easily by conserving angular momentum about point O. But I have a confusion. If we consider that rod and object as a system then we can conserve angular momentum about ##O## only if no (net) torque act on the system about point ##O##. right?

Now, torque on this system about ##O##=torque on rod about ##O## +torque on that object about ##O##. right?

When the object is just going to collide with rod. At that moment only ##Mg## force acts on the rod. But as that passes through point##O## so torque due to that force will be 0.

But when the object is just going to collide with the rod, at that moment ##Mg## force acts on the object. But it is at distance ##\frac{l}{4}## from point ##O##. And as the it falls vertically. So the torque due to that force is ##Mg\frac{l}{4}##.

So net torque on the system about point ##O## is not zero then how can we use conservation of angular momentum?