First slide

Gravitaional potential energy

Question

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances.1m, 2 m, 4 m, 8 m,.... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

Easy

A

-4G/3
B

-4G
C

-G
D

-8G/3

Solution

Resultantgravitational Potential at origin
$\large U = \frac{{ - GM}}{{{r_1}}} + \frac{{ - GM}}{{{r_2}}}\,\,\,........ = - GM\left[ {\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + ......} \right]\,\,$
$\large = - GM\left[ {\frac{1}{{1 - \frac{1}{2}}}} \right]\,\, = - 2GM = - 2 \times G \times 2 = - 4G$

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