Question

An object, of mass 5m (initially at rest), breaks up into three fragments whose masses are in the ratio 1:1:3. The two equal mass pieces fly off with equal speeds, along mutually perpendicular directions. If the speed of the heavier fragment is v, the speed of each of the other two fragments, is

(1) 3√2

(2) (√2/3)v

(3) 1.5√2v

(4) (√2/1.5)v

Answer 1

(3) 1.5√2v

Let u be the common speed of either of the two ‘equal mass’ fragments. The total momentum, of these two fragments, has a manitude

This is directed midway between the two mutually perpendicular directions. Since the total momentum, after the ‘break up’, has to again equal zero, we must have,