A satellite of mass 5M orbits the Earth in a | vedclass

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(B) Let the orbital velocity of the satellite of mass $5M$ be $v_r$. The velocities of the pieces of mass $M$ and $4M$ after the explosion are $v_1$ a

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unbound orbit

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(B) Let the orbital velocity of the satellite of mass $5M$ be $v_r$. The velocities of the pieces of mass $M$ and $4M$ after the explosion are $v_1$ and $v_4$ respectively.Given that the mass $M$ travels in the same orbit but in the opposite direction,its velocity is $v_1 = -v_r$.According to the law of conservation of linear momentum,the total momentum before the explosion is equal to the total momentum after the explosion:$5M v_r = (4M) v_4 + (M)(-v_r)$$5M v_r = 4M v_4 - M v_r$$6M v_r = 4M v_4$$v_4 = 1.5 v_r$The escape velocity for a satellite in a circular orbit is $v_e = \sqrt{2} v_r \approx 1.414 v_r$.Since $v_4 = 1.5 v_r > 1.414 v_r$,the velocity of the $4M$ mass exceeds the escape velocity.Therefore,the mass $4M$ will follow an unbound orbit (hyperbolic trajectory).

List-$I$	List-$II$
$(A)$ Kinetic energy of planet	$(1)$ $-\frac{GMm}{a}$
$(B)$ Gravitational potential energy of Sun-planet system	$(2)$ $\frac{GMm}{2a}$
$(C)$ Total mechanical energy of planet	$(3)$ $\frac{GM}{r}$
$(D)$ Escape energy at the surface of planet for unit mass object	$(4)$ $-\frac{GMm}{2a}$

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