On a horizontal smooth surface a disc is placed at rest. Another … - Vidyadip

MCQ

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 after collision first disc moves at an angle $45^o$ to the direction of motion of incoming disc :

A
$2r$
B
$r\, \left( {\sqrt 2 - 1} \right)$
✓
$\frac{r}{{\left( {\sqrt 2 - 1} \right)}}$
D
$r\,\sqrt 2 $

✓

Answer

Correct option: C.

$\frac{r}{{\left( {\sqrt 2 - 1} \right)}}$

c
$b=\left(r+r_{2}\right) \sin 45^{\circ}$

$r_{2}=\left(r+r_{2}\right) \frac{1}{\sqrt{2}}$

$\sqrt{2} r_{2}=r+r_{2}$

$(\sqrt{2}-1) r_{2}=r$

$r_{2}=\frac{r}{\sqrt{2}-1}$

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