Question

The gravitational force between two objects is F. How will the force change when
a) The distance between them is reduced to half?
b) The mass of one of the objects becomes four times?​

Answer 1

Answer:-

Given:

Gravitational force between two objects = F.

We know that,

Gravitational force = GMm/r²

where,

• G is gravitational force
• M is mass of first object
• m is mass of second Object
• r is distance between the objects.

Hence,

F = GMm/r² -- equation (1)

We have to find change in gravitational force when,

a) Distance between them is reduced to half.

→ Distance between the objects = r/2

Hence,

→ New gravitational force = GMm/(r/2)²

→ New gravitational force = GMm * (4/r²)

→ New gravitational force = (GMm/r²) * 4

→ New gravitational force = 4F N

b) Mass of one of the objects becomes 4 times.

→ Mass of first object = 4 * M = 4M

→ New gravitational force = G * 4M * m/r²

→ New gravitational force = 4 * (GMm/r²)

→ New gravitational force = 4F N

Hence, the gravitational force becomes 4 times the given value if distance between the objects is reduced to half or mass of an object becomes 4 times.

Answer 2

Answer:

According to Universal law of gravitation, the force of attraction between 2 bodies is:-

Explanation:

F = (G m1m2)/r2

Where m1m2 = the masses of the two bodies,

r = distance between them

G = gravitational Constant

When the distance is reduced to half i.e. r’ = (1/2) r then,

F’ = (G m1m2)/r2

= (G m1m2)/(r/2)2

= (4 G m1m2)/ (r2) = 4F

Therefore when the distance between the objects is reduced to half, then the force of gravitation increases by four times the original force.