Question

Three spheres (1), (2), (3) of masses M₁ (= 20 m), M₂ and M₃ (= 5 m), all lie at rest on a straigth line. Sphere (1) starts moving with a (given) speed v towards right, collides elastically with sphere (2) which, in turn then collides elastically with sphere (3). For a given value of v (and for the given values of masses M₁ and M₂ ), the maximum speed acquired by sphere (3), would be

(1) 16/9 v

(2) 18/11 v

(3) 20/13 v

(4) 22/15 v

Answer 1

Correct option is (1) 16/9 v

For an alastic collision between spheres (1) or (2), the speed acquired by sphere (2) is given by

For this value of speed of sphere (2), the speed, acquired by sphere (3), after sphere (2) collides elastically with it, is

All other factors, except M₂ are constants. Hence, for maximum value of v₃ , we need to have dv₃/dM₂ = 0

The maximum value of v₃ corresponds to this value of M₂ .