Home
Class 11
PHYSICS
Two equal spheres of mass m are in conta...

Two equal spheres of mass `m` are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on the and is reduced to rest. Prove that `e=2/3` and find the loss in `KE`.

Text Solution

Verified by Experts

Let `u` be the velocilty of sphere `A` before impact. As the spheres are identical, the triangle `ABC` formed by joining their centres is equilateral. The spheres `B` and `C` will move in directions `AB` and `AC` after impact making an angle `30^(@)` with the original line of motion of sphere `A`.
Let `v` be the speed of the other spheres after impact.

From momentum conservation,
`"mu"=mvcos30^(@)+mvcos30^(@)`
`u=vsqrt(3)`....i
From Newton's experimental law, for an oblique collision, we ahsve to take components along the normal, i.e. along `AB` for spheres `A` and `B`. Hence,
`v_(B)-v_(A)=-e(u_(B)-u_(A))`
`impliesv-0=-e(0-ucos30^(@))`
`v=eucos30^(@)`....ii
Combining eqn i and ii we get `e=2/3`
Loss in `KE =1/2"mu"^(2)-2(1/2mv^(2))`
`=1/2"mu"^(2)-m(u/sqrt3)^(2)=1/6mu^(2)`
Promotional Banner

Topper's Solved these Questions

  • CENTRE OF MASS

    CENGAGE PHYSICS|Exercise Solved Examples|13 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS|Exercise Exercise 1.1|20 Videos

  • CALORIMETRY

    CENGAGE PHYSICS|Exercise Solved Example|13 Videos

  • DIMENSIONS & MEASUREMENT

    CENGAGE PHYSICS|Exercise Integer|2 Videos

Similar Questions

Explore conceptually related problems

Two equal spheres of mass m are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and reduces to rest. Then:

Two identical billiard balls are in contact on a table. A third identical ball strikes them symmetrically and comes to rest after impact. The coefficient of restitution is :

Two billiard balls of same size and mass are in contact on a billiard table. A third ball of same mass and size strikes them symmetrically and remains at rest after the impact. Find the coefficient of restitution between the balls?

A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table. The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slippng immediately on impact, then

A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v . Find the total K.E. of the disc.

A plank of mass m_1 with a uniform sphere of mass m_2 placed on it rests on a smooth horizontal plane. A constant horizontal force F is applied to the plank. With what acceleration will the plank and the centre of the sphere move provided there is no sliding between the plank and the sphere?