Question

The gravitational force of attraction between objects A and B is $F$. If the distance between A and B is halved, then the magnitude of gravitational force between them will become

• A. $F/4$
• B. $8F$
• C. $4F$
• D. $F/2$

Answer 1

The correct option is C $4F$

Answer is C.

The force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as

$F\propto \frac{m_1.m_2}{d^2}$

where, $m_{1}and{m}_2$ are masses of the object and d is the distance of sepration between them.

In this case, the distance between A and B is halved. So, the gravitational force will become $F\propto \frac{m_1.m_2}{{\left(\frac{d}{2}\right)}^2},thatis,F\propto 4\frac{m_1.m_2}{d^2}$

Hence, the magnitude of gravitational force between them will become $4F$.