91Ó°ÊÓ

We need to find out :

a) The speed and direction of each ball after the collision in case of Elastic collision

b) The speed and direction of the combined balls after the collision in case of Inelastic Collision

Velocity of object 1 in lab = v_1L = 4 m/s

Velocity of object 2 in lab = v_2L= -3 m/s

If velocity of object 2 in frame = v_2M = 0

So velocity of frame w.r.t lab = v_ML = -3 m/s

Velocity of lab w.r.t frame = v_LM = 3 m/s

Therefore,

Velocity of object 1 in frame M = v_1M = v_1L + v_LM = 4 + 3

= 7 m/s

Using formula in case of elastic collision for velocities,

$$\begin{gathered} v_{1Mf}=\frac{m_1-m_2}{m_1+m_2}{v}_{1M} \\ =\frac{0.1-0.2}{0.1+0.2}×7=-2.33m/s \\ {v}_{2Mf}=\frac{2m_1}{m_1+m_2}{v}_{1M} \\ =\frac{2×0.1}{0.1+0.2}×7=4.67m/s \end{gathered}$$

Converting them into Lab frame,

v_1Lf = v_1Mf + v_ML

= -2.33 + (-3)

= -5.33 m/s

v_2Lf = v_2Mf + v_ML

= 4.67 - 3

= 1.67 m/s

We know that in case of Inelastic collision,

$$\begin{gathered} (m_1+m_2)v_f=m_1{v}_1+m_2{v}_2 \\ (0.1+0.2)v_f=0.1×4+0.2×(-3) \\ 0.3v_f=0.4-0.6=-0.2 \\ {v}_f=-\frac{0.2}{0.3}=-0.67m/s \end{gathered}$$

(Negative sign indicates that they will move together towards Left)