Two bodies of mass M each are placed R distance apart. In another system, two bodies of mass 2M each are placed $\frac{R}{2}$ distance apart. If F be the gravitational force between the bodies in the first system, then the gravitational force between the bodies in the second system will be
16 F
1 F
4 F
None of the above
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC NDA-2 – 2019
In the first system: $m_1 = M$, $m_2 = M$, $R_1 = R$. The force is $F_1 = G \frac{M \times M}{R^2} = G \frac{M^2}{R^2}$. This force is given as F. So, $F = G \frac{M^2}{R^2}$.
In the second system: $m_1′ = 2M$, $m_2′ = 2M$, $R_2 = R/2$. The force is $F_2 = G \frac{(2M) \times (2M)}{(R/2)^2}$.
Calculate $F_2$: $F_2 = G \frac{4M^2}{R^2/4} = G \frac{4M^2}{R^2} \times 4 = 16 G \frac{M^2}{R^2}$.
Substitute the expression for F: $F_2 = 16 F$.