Question

Three particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is

• A. zero
• B. $ \frac{3GM}{{{L}^{2}}} $
• C. $ \frac{9GM}{{{L}^{2}}} $
• D. $ \frac{12}{\sqrt{3}}\frac{GM}{{{L}^{2}}} $

Answer 1

Answer: (A)

The net force acting on a unit mass placed at $ O $ due to three equal masses $ M $ at vertices $ A,\,\,B $ and $ C $ is the gravitational field intensity at point $ O $ . The gravitational force on the particle placed at the point of intersection of three medians.
$ \overset{\to }{\mathop{{{F}_{1}}}}\,+\overset{\to }{\mathop{{{F}_{2}}}}\,+\overset{\to }{\mathop{{{F}_{3}}}}\,=0 $ Since, the resultant of $ \overset{\to }{\mathop{{{F}_{1}}}}\, $ and $ \overset{\to }{\mathop{{{F}_{2}}}}\, $ is equal and opposite to $ \overset{\to }{\mathop{{{F}_{3}}}}\, $ .