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 , y_{cm} = 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