Question

the particles A and B of mass m each are separated by a distance r.Another particle C of mass M is placed at the midpoint of A and B.Find the work done in taking C to a point equidistant r from A and B without acceleration.​

Answer 1

Answer:

Work done will equal to change in gravitational potential energy

$w =2 \times G \frac{Mm}{ \frac{r}{2} } - 2 \times G \frac{Mm}{r} \\ \\ w = \frac{2GMm}{r}$

Answer 2

Without acceleration, there will be no work done. The work done is given below in the terms of gravitational attraction.

Explanation:

First we need to find the distance traveled by the particle C,

                              Take it h = $\sqrt{r^{2} - \frac{r}{2} ^{2} }$

                                      ⇒ h = $\frac{\sqrt{3 }\times r }{2}$

So, gravitational force,

                                       ⇒ F = $\frac{GMm}{h^{2} }$

                                      ⇒ F = $\frac{GMm}{\frac{3r^{2}}{4} }$

                 

                            ⇒ Work done = F x h

                            ⇒ W = $\frac{GMm}{\frac{\sqrt{3} r}{2} }$

In this form work can be done through gravitational attraction. But, in opposite direction, not away from the points A and B.