*Do not worry about your problems with mathematics; I assure you mine are far greater.*

– Albert Einstein

An object of mass *m* collides* elastically* with the lower end B of a thin uniform rod AB of mass 3*m* and length *L *suspended vertically using a frictionless hinge at its upper end A (Fig.) so that it can rotate in a vertical plane. The only external force present is that of earth’s gravity. Just before collision the object was moving horizontally with speed *v*. Now answer the following questions:

(a) Given that the moment of inertia of a thin uniform rod of mass *M* and length *L *about an axis passing through its middle and perpendicular to its length is *ML*^{2}/12, determine the moment of inertia of the rod AB about the hinge.

(b) Calculate the horizontal speed of the object of mass *m *after* *the collision.

(c) Suppose the colliding object were of the same mass (3*m*) as that of the rod. Calculate the distance *d* from the hinge at which the colliding object (moving with the horizontal speed *v*)* *should hit the rod so that its kinetic energy is fully transferred to the rod. * *

(d) If the collision at the position obtained in part (c) is such that the colliding object gets attached to the rod, calculate (in terms of the given parameters) the angular velocity with which the rod starts moving after the collision

The above question carries 15 points and you have 15 minutes at your disposal. Try to answer this question. I’ll be back soon with a model answer for your benefit.

You can find other posts involving rotation on this site (including equations to be remembered) by clicking on the

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