Question

Assertion : When distance between two bodies is doubled and also mass of each body is doubled, gravitational force between them remains the same.
Reason : According to Newton’s law of gravitation, force is directly proportional to product of the mass of bodies and inversely proportional to the square of the distance between them.

• A. If both assertion and reason are true and reason is the correct explanation of assertion
• B. If both assertion and reason are true but reason is not the correct explanation of assertion
• C. If assertion is true but reason is false
• D. If both assertion and reason are false

Answer 1

Answer: (A)

According to Newtons law of gravitation, $F = \frac{Gm_{1}m_{2}}{r^{2}}$. When $m_{1}$, $m_{2}$ and $r$ all are doubled, $F= \frac{G\left(2m_{1}\right)\left(2m_{2}\right)}{\left(2r\right)^{2}} = \frac{Gm_{1}m_{2}}{r^{2}}$, i.e. $F$ remains the same.