Two perfectly elastic objects and of identical mass are moving with velocities 15 m/s and 10 m/s respectively, collide along the direction of line ioining
them. Their velocities after collision are respectively
 

 IN  a perfectly elastic collision if the colliding bodies or particles have equal masses then after collision they will exchange their velocities.

 Let m be the identical mass of two objects ,1 and B we have 

$$\begin{gathered} 15\mathrm{m}+10\mathrm{m}={\mathrm{mv}}_1+{\mathrm{mv}}_2 \\ 25={\mathrm{v}}_1+{\mathrm{v}}_2 \\ \mathrm{In} \mathrm{elastic} \mathrm{collision}, \\ \frac{{\mathrm{v}}_2-{\mathrm{v}}_1}{{\mathrm{u}}_1-{\mathrm{u}}_2}=1\text{ or }\frac{{\mathrm{v}}_2-{\mathrm{v}}_1}{15-10}=1 \\ \therefore {\mathrm{v}}_2-{\mathrm{v}}_1=5 \\ \mathrm{Solving} \mathrm{eqs}. \left(1\right) \mathrm{and} \left[2\right), \mathrm{we} 8\mathrm{et} \\ {\mathrm{V}}_2=15\mathrm{m}/\mathrm{s}\text{ and }{\mathrm{v}}_1=10\mathrm{m}/\mathrm{s} \end{gathered}$$