Question

Two buckets each of mass 6kg are connected on each of a light inextensible string going over a smooth pulley.A piece of putty of mass 2kg is dropped through a height of 2m into one bucket and becomes attached .Calculate the velocity and the velocity of the system after impact

Answer 1

Speed of the falling mass:

$$v=\sqrt{2gh}.$$

This mass is attached to a bucket, which is connected to another bucket. So, we can say that this mass is attached to both buckets. Application of momentum conservation gives us the following:

$$0+mv=2Mu,\\\space\\ u=\frac{mv}{2M}=\frac{m\sqrt{2gh}}{2M}=1.04\text{ m}.$$