Two equal spheres $B$ and $C$ , each of mass m, are in contact on a smooth horizontal table. A third sphere A of same size of that of $B$ or $C$ but mass $m / 2$ impinges symmetrically on them with a velocity u and is itself brought to rest. The coefficient of restitution between the two spheres $A$ and $B$ (or between $A$ and $C$ ) is :

1 / 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1 / 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 / 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 / 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1 / 3$
$L e t t h e i n i t i a l v e l o c i t y o f m a s s \frac{m}{2} b e u a n d f i n a l v e l o c i t i e s o f m a s s e s m b e e a c h v b e c a u s e o f s y m m e t r y . F i n a l v e l o c i t y o f t h e t w o m a s s e s w i l l b e a l o n g t h e d i r e c t i o n o f i m p a c t . C o n s e r v a t i o n o f m o m e n t u m s a y s \frac{m}{2} u = 2 m v c o s 30^{0} a n d c o e f f i c i e n t o f r e s t i t u t i o n s a y s v - 0 = - e (0 - u c o s 30^{0}), s o l v i n g t h e s e w e g e t e = \frac{1}{3}$

Suggest Corrections

Similar questions

Two equal spheres of mass $m$ are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E

Q. Two equal spheres of mass

m

are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Prove that

e = 2 / 3

and find the loss in KE.

Two equal spheres of mass $m$ are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E

Q. Sphere of mass