Question

A sphere of mass m moving horizontally V0 collides against a pendulum bob of mass m. If the two masses stick together after the collision then the maximum height attained is

Answer 1

Hopefully this will help you

Answer 2

Answer:

The maximum height attained after collision is  $\frac{v_{0}^{2}}{8g}$.

Explanation:

Given mass of sphere =  m

Initial velocity of sphere = $v_{0}$

Mass of pendulum bob =  m

And two masses stick together after the collision

Since the pendulum is at rest, its initial velocity is zero.

According to the law of conservation of momentum, momentum before collision is equal to momentum after collision.  

Therefore, $mv_{0} =(m +m)v$

$\implies mv_{0} =2mv\implies v_{0} =2v$

Kinetic energy of the combined masses after collision is

$\frac{1}{2} (2m)v^{2} =m (\frac{v_{0}}{2} )^{2}$

Let the system reached the maximum height, h.

then the potential energy of the system $=2mgh$

Applying the law of conservation of energy, kinetic energy is equal to potential energy.  

Therefore, $m (\frac{v_{0}}{2} )^{2} =(2m)gh$

$\implies\frac{v_{0}^{2}}{4} =2gh\implies h=\frac{v_{0}^{2}}{8g}$

Hence, the maximum height attained is  $\frac{v_{0}^{2}}{8g}$.