Question

If three particles, each of mass M, are placed at the three corners of an equilateral triangle of side a, the forces exerted by this system on another particle of mass M placed (i) at the midpoint of a side and (ii) at the centre of the triangle are, respectively.

• A. $0,\frac{4G{M}^2}{3a^2}$
• B. $\frac{4G{M}^2}{3a^2},0$
• C. $\frac{3G{M}^2}{a^2},\frac{G{M}^2}{a^2}$
• D. $0,0$

Answer 1

The correct option is B $\frac{4G{M}^2}{3a^2},0$

(i) (Refer to Image 1)

$F=\frac{GMM}{{\left(\frac{a\sqrt{3}}{2}\right)}^2}=\frac{4}{3}\frac{G{M}^2}{a^2}$

(ii) (Refer to Image 2) as net force $0$

Answer is , $\frac{4G{M}^2}{3a^2},0$ .