An insulated particle of mass `m` is moving in a horizontal plane (x - y) along X-axis. At a certain height above the ground, it suddenly explodes into two fragments of masses `m//4 and 3 m//4`. An instant later, the smaller fragment is at `Y = + 15`. The larger fragment at this instant is at :

Explanation

As isolated particle is moving along x-axis at a certain height above the ground, there is no motion along Y-axis. Further, the explosion is under internal forces only. Therefore, centre of mass remains stationary along Y-axis after collision. Let the co-ordinates of centre of mass be `(x_(cm),0)`.
Now, `y_(cm) = (m_(1)y_(1) + m_(2)y_(2))/(m_(1) + m_(2)) = 0`
`:. m_(1)y_(1) + m_(2)y_(2) = 0`
or `y_(2) = (-m_(1)y_(1))/(m_(2)) = (-m//4)/(3m//4) xx 15 = - 15 cm`
`:.` Large fragment will be at `y =- 5 cm` :
along x-axis.