Question

There are two bodies which attracts each other with a certain mutual force. If the distance is made ⅓ times, then the force between them will become :

• A. nine times
• B. three times
• C. ⅓ times
• D. ⅑ times

Answer 1

Answer:

A. nine times

The force of attraction between two bodies due to gravity is described by Newton's Law of Universal Gravitation,

which states that the gravitational force FF between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

This can be expressed as:

F=G⋅m1⋅m2

r²

Where:

• F is the gravitational force,

• G is the gravitational constant,

• m1 and m2 are the masses of the two bodies,

• r is the distance between the centers of the two bodies.

If the distance between the two bodies is reduced to 1/3 of its original value, the new force ′F' can be calculated as:

F= G⋅m1⋅m2 = G⋅m1⋅m2 = 9 . G⋅m1⋅m2 = 9. F

( r²/3)² r²/9 r²

Therefore, if the distance is reduced to one-third, the gravitational force will indeed become nine times stronger.