First slide

Gravitaional potential energy

Question

The masses, each of mass m are kept on the vertices of an equilateral triangle of side a. Find the work needed to be done to change the length of each side of the triangle twice of its original value.

Easy

A

$\frac{{Gm}^{2}}{3 a}$
B

$- \frac{3 {Gm}^{2}}{a}$
C

$\frac{3 {Gm}^{2}}{2 a}$
D

$- \frac{3 {Gm}^{2}}{2 a}$

Solution

By the work-energy theorem we can write that
$\begin{array}{l} W_{ext} + W_{gr} = Δ (K . E) = 0 \\ \Rightarrow W_{ext} = - W_{gr} = - (- ΔU) = ΔU \end{array}$
$\begin{array}{l} W_{ext} = - \frac{3 {Gm}^{2}}{2 a} - (- \frac{3 {Gm}^{2}}{a}) \\ = \frac{3 {Gm}^{2}}{2 a} \end{array}$

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