Question

Particles each of mass M are placed along x-axis at $x=1m,x=2m,x=4m,x=8m$ etc to infinity. Gravitational field strength at the origin due to this system of particles is?

• A. $2$GM
• B. $2$GM$/3$
• C. $4$GM$/3$
• D. $5$GM$/4$

Answer 1

The correct option is C $4$GM$/3$

Gravitational field at a distance $x$ due to a point mass $M$ is given by $E=\frac{GM}{x^2}$

So, net gravitational field $E_{net}=E_1+E_2+E_3+.......\infty terms$

Or $E_{net}=\frac{GM}{x_1^2}+\frac{GM}{x_1^2}+\frac{GM}{x_3^2}+.........$

Or $E_{net}=\frac{GM}{1^2}+\frac{GM}{2^2}+\frac{GM}{4^2}+.........$

Or $E_{net}=GM[\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{4^2}+.........]$

Or $E_{net}=GM\times \frac{1}{(1-\frac{1}{4})}=\frac{4GM}{3}$

Correct answer is option C.