A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms$-$1 and 40 ms$-$1 respectively. The velocity of the third piece will be :

Question

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^$-$1 and 40 ms^$-$1 respectively. The velocity of the third piece will be :

15 ms^$-$1