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 as 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

Two equal spheres B and C, each of mass m, are in contact on a smooth

1.	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 as 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
Answer» `1//3` `1//4` `2//3` `3//4` Solution :`u=`velocity 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 DIRECTION `AB` and `AC` after impact making can ANGLE of `30^(@)` with the origina lines of motion of BALL `A`. Let `v` be the speed ofthe balls `B` and `C` after impact. Momentum conservationgives `(m/2)u=mvcos30^(@) +mvcos30^(@)` `u=2sqrt(3)vimpliesv=u/(2sqrt(3))`.......i From Newton's experimental law, for an oblique collision, we have take components along normal, i.e. along `AB` for balls `A` and `B`. `v_(B)-v_(A)=-e(u_(B)-u_(A))` `v-0=-e(0-ucos30^(@))` `v=eucos30^(@)`.........ii Combining EQN i and ii we get `e=1/3` Loss in `KE =1/2 m/2 u^(2)-2(1/2mv^(2))` `=1/4mu^(2)-m(u/(2sqrt(3)))^(2)=1/6mu^(2)`