Question

Two particles of mass m and m are initially at rest and infinitely separated from each other. due to mutual interaction they approach each other. their relative velocity of approach at a distance of separation d between them is

Answer 1

Force between them, F = Gm×m/d^2
where d is the separation distance and G is the Universal Gravitational Constant.

F=Gm^2/d^2

F = ma for each particle, (acc to Newton's Second Law of Motion). where a is acceleration of a particle.

Now F/m = a

Now integrating both sides, we can obtain

$\int \frac{F}{m} dt = \int a dt$
or, $\frac{F}{m} \times t = v$

Gravitational force is a conservative force.
(v is velocity).

v = Ft/m

where t denotes time.

Answer 2

Answer:

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