Question

Reason
The energy of the earth-satellite system in a circular orbit is given by $$E = ( -GMm) / (2r) $$, where r is the radius of the circular orbit.
Assertion
Two satellites are following one another in the same circular orbit. If one satellite tries to catch another (leading one) satellite, then it can be done by increasing its speed without changing the orbit.
Two satellites are following one another in the same circular orbit. If one satellite tries to catch another (leading one) satellite, then it can be done by increasing its speed without changing the orbit.

Answer 1

Correct option is C. Assertion is incorrect but Reason is correct
As we know,

$$E=\dfrac{1}{2} mv^2-\dfrac{GM}{r}$$

and $$v=\sqrt{\dfrac{GM}{r}}$$

so,

$$E=-\dfrac{GMm}{2r}$$

so, statement (ii) is correct and,

Here Statement 1 is incorrect because as speed of one satellite increases, its kinetic energy and hence total energy increases, i.e., total energy becomes less negative and hence r increases,

i.e. orbit changes.

hence,

option C is correct.