Question

On a horizontal smooth surface a disc is placed at rest. Another disc of same mass is coming with impact parameter equal to its own radius. First disc is of radius $r$. What should be the radius of coming disc so that disc moves at an angle ${45}^{\circ }$ to the direction of motion of incoming disc.

• A. $2r$
• B. $r(\sqrt{2}-1)$
• C. $\frac{r}{(\sqrt{2}-1)}$
• D. $r\sqrt{2}$

Answer 1

The correct option is C $\frac{r}{(\sqrt{2}-1)}$

$\sin {45}^0=\frac{R}{R+r}$

$\frac{1}{\sqrt{2}}=\frac{R}{R+r}$

$(\sqrt{2}-1)R=rR=\frac{r}{(\sqrt{2}-1)}$