Question

If the gravitational force between two bodies of mass $M_1$ and $M_2$ and situated at a distance R is F, then find the force F' between them at distance $(R+D)$

• A. $F^{\prime }=\frac{R^{}F}{(R+d{)}^2}$
• B. $F^{\prime }=\frac{R^{2}F}{(R+d{)}^{}}$
• C. $F^{\prime }=\frac{R^{2}F}{(R+d{)}^2}$
• D. $F^{\prime }=\frac{F}{(R+d{)}^2}$

Answer 1

The correct option is C $F^{\prime }=\frac{R^{2}F}{(R+d{)}^2}$

$F=\frac{{GM}_1{M}_2}{R^2}$

$R\to R+d$

$\therefore F^{\prime }=\frac{{GM}_1{M}_2}{{(R+d)}^2}=\frac{{GM}_1{M}_2}{R^2{(R+d)}^2}{R}^2$

$=\frac{{FR}^2}{{(R+d)}^2}$