Question

3) A body of mass 2.0 kg makes an elastic collision
with another body at rest and continues to move
in the original direction with a speed equal to half
its original speed. Find the mass of the second
body.
​

Answer 1

4kg

Explanation:

mv=constant

2v=mv/2m

m=4kg

Answer 2

ANSWER:

The mass of the second body is 2 kg.

EXPLANATION:

As the body collides with another body at rest in elastic collision so the momentum will be conserved before and after collision. Thus the body obeys law of conservation of momentum.  

According to law of conservation of momentum, the momentum of bodies before collision will be equal to the momentum of the bodies after collision.

$M u_{1}+m u_{2}=M v_{1}+m v_{2}$

Here M is the moving body whose mass is given as 2 kg, u1 and v1 are initial and final velocities of the first body which is moving. The symbols m, u2 and v2 represents the mass, initial and final velocities of second body.  

As it is stated that after colliding with the second body, the speed of the first body get reduced to half of its original speed which means the other half is transferred to the second body on collision due to the collision being an elastic collision. Thus the "initial velocity" of first body will be u1, "final velocity" of the first body after collision will be $\mathrm{v}_{1}=\mathrm{u}_{1} / 2$. Similarly, the "initial velocity" of the second body u2 will be zero and the "final velocity" of the second body after collision will be $\mathrm{v}_{2}=\mathrm{u}_{1} / 2$.

Thus the mass of the second body can be determined as follows:

$2 u_{1}+(m * 0)=\frac{2 u_{1}}{2}+m \frac{u_{1}}{2}$

$2 u_{1}=u_{1}+\frac{m u_{1}}{2}$

$2 u_{1}-u_{1}=\frac{m u_{1}}{2}$

$u_{1}=\frac{m u_{1}}{2}$

 Thus the mass of second object is also 2 kg.