Question

On a frictionless surface, a block of mass $M$ moving at speed $\upsilon$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $\frac{\upsilon }{3}$. The second block's speed after the collision is

• A. $\frac{\sqrt{3}}{2}\upsilon$
• B. $\frac{2\sqrt{2}}{3}\upsilon$
• C.
  $\frac{3}{4}\upsilon$
• D.
  $\frac{3}{\sqrt{2}}\upsilon$

Answer 1

The correct option is B $\frac{2\sqrt{2}}{3}\upsilon$

Using energy conservation, $\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_2{v}_2^2=\frac{1}{2}{m}_{1}v{{}_1^{\prime }}^2+\frac{1}{2}{m}_{2}v{{}_2^{\prime }}^2$
Here, $\frac{1}{2}M{v}^2+0=\frac{1}{2}M(v/3{)}^2+\frac{1}{2}Mv{{}_2^{\prime }}^2$
or $v{{}_2^{\prime }}^2=\frac{8}{9}{v}^2$
or $v{}_2^{\prime }=\frac{2\sqrt{2}}{3}v$