Question

the distance between them is increased by $50$% (other factors are kept same)

• A. $\frac{5}{9}F$
• B. $\frac{4}{9}F$
• C. $\frac{1}{9}F$
• D. $\frac{4}{5}F$

Answer 1

The correct option is B $\frac{4}{9}F$

Gravitational Force $F=\frac{G{m}_1{m}_2}{r^2}$,

$\therefore F=\frac{G{m}^2}{a^2}$

Now distance is increased by 50% and other factors kept constant. $\Rightarrow a$'= $1.5a$,

So New $F$'= $\frac{G{m}^2}{(1.5a{)}^2}$ $\Rightarrow F$'= $\frac{4}{9}F$