Question

A particle of mass $3m$ is projected from point $A$ with speed $3v_0$ as shown in the figure. When the particle is at the point $P$, it explodes in three identical particles. Choose the INCORRECT statement regarding the physical quantities just before and just after the explosion.

• A. The linear momentum of system can be conserved just before and just after explosion
• B. The centre of mass of the system will trace same path as it will follow without explosion
• C. The mechanical energy of the system remains conserved just before and just after explosion
• D. The impulse given by the weight of particle during explosion is negligible as compared to that by the explosive forces.

Answer 1

The correct option is C The mechanical energy of the system remains conserved just before and just after explosion

In any explosion centre of mass is move with constant speed as before and after and momentum is conserved. For example, if m break into two equal part initial velocity = v. Then a

By momentum conservation final velocity = u.

$u=\frac{m}{\left(\frac{m}{2}\right)}v=2v$

Mechanical energy before explosion $=\frac{1}{2}m{v}^2$

after explosion $=\frac{1}{2}\times \frac{m}{2}(2v{)}^2$

$=m{v}^2$

Mechanical energy not conserves in the explosion because in explosion energy release.