Question

A Shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in
A. vertical direction
B. any direction
C. horizontal direction
D. same parabolic path

Answer 1

Hint:The net force applied in an explosion is zero. Newton’s second law states that the net force applied is equal to the mass times acceleration of the body.We know that the acceleration of a body is given by Newton's second law. It states that the acceleration of a body is the ratio of the net force applied on the body to the mass of the body.

Complete step by step answer:
The mathematical expression is given by,
\[a = \dfrac{F}{m}\]
where,\[F\] is the net force applied to the body, \[m\] is the mass of the body and \[a\] is the acceleration of the centre of mass of the body.

Now, when a body explodes in multiple parts the net force applied due the explosion is zero.Hence, net acceleration of the system or the centre of mass of the system must be zero since applied force is zero. Since, \[F = 0\] so, \[a = 0\]. So, when the body is moving in a parabolic path and it explodes in the middle of the path the acceleration of the system due to the acceleration must be zero. Hence the centre of mass of the system must be moving in the same path as before, since no extra force has been applied.

Hence, the correct answer is option D.

Note: If the body explodes in two parts from conservation of momentum we can write, \[Mv = {m_1}{v_1} + {m_2}{v_2}\] and the centre of mass of the system is given by, \[R = \dfrac{{{m_1}{r_1} + {m_2}{r_2}}}{M}\]. So, differentiating the equation we can easily see that, the velocity of the centre of mass of the body is equal to the momentum velocity of the body before collision.