Question

If the distance between sun and earth is made $3$ times of the present value, then gravitational force between them will become :

• A. $9$ times present value
• B. $\frac{1}{9}$ times present value
• C. $\frac{1}{3}$ times present value
• D. $3$ times present value

Answer 1

The correct option is B $\frac{1}{9}$ times present value

According to Newton’s law of gravitation, the force between the sun and earth is given by $F=\frac{GMm}{r^2}$

$\Rightarrow F\propto \frac{1}{r^2}$

When the distance between the sun and earth is three times the original distance, then
$\frac{F}{F^{\prime }}=\frac{r^{\prime 2}}{r^2}=9$

$\Rightarrow F^{\prime }=\frac{F}{9}\text{units}$

Hence, option (b) is the correct answer.