Question

A ball strikes a wall with a velocity $\overrightarrow{u}$ at an angle $\theta$ with the normal to the wall surface and rebounds from it at an angle $\beta$ with the surface. Then:

• A. If wall is smooth, $(\theta +\beta )$ > ${90}^{\circ }$
• B. If the wall is smooth, coefficient of restitution $=\frac{tan\beta }{cot\theta }$
• C. If wall is smooth, coefficient of restitution < $\frac{tan\beta }{cot\theta }$
• D. None of these

Answer 1

The correct option is B

If the wall is smooth, coefficient of restitution $=\frac{tan\beta }{cot\theta }$

Velocity v cos $\beta$ = u sin $\theta$ . . . (i)

$vsin\beta =e.u‘cos\theta$ . . . (ii)

from the above equation, tan $\beta =ecot\theta$

$ortan\beta =etan({90}^{\circ }-\theta )$

$\beta <(90-\theta )$

$or(\beta +\theta )<{90}^{\circ }$

$e=\frac{tan\beta }{tan\theta }$, Hence, (b) is the correct choice