If the Moon is brought closer to the Earth such that its distance from the Earth becomes half of the original distance, then the gravitational force of attraction between the Earth and the Moon would :
reduce to half of its original value.
increase to two times of its original value.
remain the same as the original value.
increase to four times of its original value.
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CDS-2 – 2023
In this case, M₁ is the mass of the Earth (M_earth) and M₂ is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G * (M_earth * M_moon) / r².
If the distance is halved, the new distance is r’ = r/2. The new gravitational force F’ will be:
F’ = G * (M_earth * M_moon) / (r’)²
F’ = G * (M_earth * M_moon) / (r/2)²
F’ = G * (M_earth * M_moon) / (r²/4)
F’ = 4 * [G * (M_earth * M_moon) / r²]
So, F’ = 4 * F. The gravitational force increases to four times its original value.