Q: An isolated particle of mass m is moving in horizontal plane (X-Y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragment of masses m/4 and 3m/4. An instant later, the smaller fragment is at y = +15 cm. The larger fragment at this instant is at
(a)Y=-5 cm
(b)Y=+20 cm
(c)Y=+5 cm
(d)Y=-20 cm
Ans: (a)
Sol: Before explosion , particle was moving along X-axis .Hence Y component of velocity is zero . Therefore centre of mass will not move along Y direction , ycm = 0
$\large y_{cm} = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2}$
$\large 0 = \frac{(m/4)\times 15 + (3m/4)\times Y}{m/4 + 3m/4}$
Y = – 5 cm