Question

Two equal point masses are separated by a distance $d_{1}$. The force of gravitation acting between them is $F_{1}$. If the separation is decreased to $d_{2}$, then the new force of gravitation $F_{2}$ is given by

• A. $F_{2}=F_{1}$
• B. $F_{2}=F_{1}\left(\frac{d_{1}}{d_{2}}\right)^{2}$
• C. $F_{2}=F_{1}\left(\frac{d_{2}}{d_{1}}\right)^{2}$
• D. $F_{2}=F_{1}\left(\frac{d_{1}}{d_{2}}\right)$

Answer 1

Answer: (B)

From Newton's law of gravitation, the two equal point masses are separated by a distance $d_{1}$ is shown below

Gravitational force, $F_{1}=\frac{G m \cdot m}{d_{1}^{2}}=\frac{G m^{2}}{d_{1}^{2}}$ ....(i)
Similarly,

Gravitational force, $F_{2}=\frac{G m^{2}}{d_{2}^{2}}$ .... (ii)
On dividing Eq. (i) by Eq. (ii), we get
$ \frac{F_{1}}{F_{2}} =\left(\frac{d_{2}}{d_{1}}\right)^{2} $
$\therefore F_{2} =F_{1}\left(\frac{d_{1}}{d_{2}}\right)^{2}$