Question

A bomb kept at rest on a smooth horizontal surface, suddenly explodes then identify the correct statement:

• A. $\text{COM}$ of bomb will remain at rest.
• B. $\text{COM}$ of bomb will move along the surface with a constant velocity after the explosion.
• C. After explosion, all the fragments of bomb will fly in vertically upwards direction.
• D. Explosion of bomb will cause the centre of mass of bomb to accelerate.

Answer 1

The correct option is A $\text{COM}$ of bomb will remain at rest.

From the newton's law for system of particles,,
$F_{\text{ext}}=m{a}_{\text{CM}}$
$\Rightarrow$when bomb explodes the forces responsible for explosion are internal forces.
The only external forces acting on bomb is normal reaction $N$ from surface and its weight $mg$ downwards.
$\because$bomb is at rest initially , so $N=mg$ in vertical direction. External horizontal force is absent on bomb hence net $F_{\text{ext}}=0$.
$\therefore a_{\text{CM}}=0$, hence applying kinematics equation on $COM$ of bomb:
$S_{\text{CM}}=u_{\text{CM}}t+\frac{1}{2}{a}_{\text{CM}}{t}^2$
$S_{\text{CM}}=0+\frac{1}{2}\times 0\times t^2=0$
$\Rightarrow$ Hence centre of mass of bomb will remain at rest even after explosion.
Now,
$v_{\text{CM}}=u_{\text{CM}}+a_{\text{CM}}t=0+0=0$
it represents that final velocity of centre of mass is zero, so $COM$ of bomb will not move along the surface.

$\Rightarrow$After the explosion, all the fragements will move in different directions, such that momentum of system remains constant at $\text{Zero}$.
$P_i=P_f=m{v}_{\text{CM}}=m\times 0=0$