Correct Answer - Option 2 : 300%
Concept:
-
Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.
It is given mathematically as follows:
\(F = \frac{Gm_1m_2}{R^2}\)
Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.
- The gravitational constant G establishes a relationship between gravitational force, mass, and distance.
- The value of G is 6.67 × 10-11 N kg-2 m2.
Calculation:
At present, let the force be (By Law of Gravitation)
\(F = \frac{Gm_1m_2}{R^2}\) ---(1)
If the distance is halved, the new distance is R' = R / 2
Then the new force is
\(F' = \frac{Gm_1m_2}{R'^2}\)
⇒ \(F' = \frac{Gm_1m_2}{(R/2)^2}\)
⇒ \(F' = \frac{Gm_1m_2}{(R^2/4)}\)
⇒ \(F' =4 \frac{Gm_1m_2}{(R^2)}\) ---(2)
From (1) and (2)
⇒ F' = 4 F
Change in Force F' - F = 4 F - F = 3 F
Percentage change in Force
\(\Delta P = \frac{\Delta F}{F} \times 100 \% = \frac{F' - F}{F}\%\)
⇒ \( \Delta P= \frac{4F - F}{F} 100\% = 300 \%\)
So, the correct option is 300 %.
