Question

gravitational force between two objects is F. How will the force change when the distance between them is reduced to 1/4 th ?​

Answer 1

Given,

Gravitational force between two objects is F.

To Find,

Change  in force when distance is reduced to 1/4th.

Solution,

Gravitational force is inversely proportional to distance and directly proportional to product of two masses.

So, F=Gm1.m2/r²

Distance between them is reduced to 1/4th

So r will be r/4 then

r² will r/16

So new force will be,

F'=Gm1m2/(r²/16)

  =16(gm1m2/r²)

  =16F

Hence, force will be multiplies of 16 when distance between them is reduced to 1/4.

Answer 2

Answer:

The gravitational force between two objects becomes 16 times on reducing r to r/4

Explanation:

we know gravitational field did inversely proportional to the distance between the object and directly proportional to the product of masses.

gravitational force  

$F = G \frac{mM}{r^{2} }$

Given: distance is reduced to 1/4th.

force when distance is r

$F = G \frac{mM}{r^{2} }$

distance is reduced to

1/4 r'= r/4

the force with reduced distance substituting r' from above

$F'= G \frac{mM}{r'^{2} }\\ \\F'= G\frac{16mM}{r^{2} } \\\\F'=16F$

Hence gravitational force between two objects becomes 16 times on reducing the distance between them