Question

A ball of mass 2.4kg suffers an elastic headon collision with another ball at rest . After collision , the ball a continues moving in the same direction with a speed 1/5 of its original speed will ball b starts moving forward. Find the mass of the ball b

Answer 1

Answer:

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Answer 2

The mass of the ball b is 1.608 kg .

Mass of ball A , $m_a=2.4\ kg$ .

Let , initial speed of ball A is $u_a$ and final speed of ball B is $u_b$ .

Also , let mass of ball B is $m_b$ .

It is given that the collision is elastic .

Therefore , Kinetic energy is conserved .

So ,

$\dfrac{m_au_a^2}{2}+0=\dfrac{m_bu_b^2}{2}+\dfrac{m_a(\dfrac{u_a}{5})^2}{2}\\\\\dfrac{24m_au_a^2}{25}=m_{b}u_b^2$ ...... ( 1 )

Also , applying conservation of momentum , we get :

$mu_a+0=m\dfrac{u_a}{5}+mu_b\\\\\dfrac{4m_{a}u_a}{5}=m_{b}u_b$        ....... ( 2 )

Solving equation 1 and 2 by divding :

We get :

$m_b=0.67m_a\\\\m_b=0.67\times2.4\\\\m_b=1.608\ kg$

Hence , this is the required solution .

Learn More :

Conservation of Momentum

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