Question

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be

• A. $\frac{2}{9}F$
• B. $\frac{16}{9}F$
• C. $\frac{8}{9}F$
• D. $F$

Answer 1

Answer: (C)

$\frac{8}{9}F$

Answer 2

Let the masses are m and distance between them is l, then
F=$\frac{Gm^2}{I^2}$

When $\frac{1}{3^{rd}}$ mass is transferred to the other then masses will be $\frac{4m}{3}$ and $\frac{2m}{3}$.

So new force will be

F′=G\frac{4m}{3}$$\frac{G\frac{4m}{3}×\frac{2m}{3}}{I^2}

=\frac{8}{9}$$\frac{Gm^2}{I^2}

=$\frac{8}{9}F$

$\therefore ,$ The correct option is (C): $\frac{8}{9}F$