Question

the gravitational force of attraction between two bodies at a distance x is 20 n what will be the force of attraction between them if the distance between them is made 2x

Answer 1

$\large{\underline{\underline{\mathfrak{\green{\sf{Question:-}}}}}}$.

• the gravitational force of attraction between two bodies at a distance x is 20 n what will be the force of attraction between them if the distance between them is made 2x.

$\large{\underline{\underline{\mathfrak{\bf{Given\:Here:-}}}}}$.

• Force of attraction between two bodies= 20N

• Distance between two bodies = x

$\large{\underline{\underline{\mathfrak{\sf{Find\:here:-}}}}}$.

• Force of attraction, when distance between two bodies is 2x.

$\large{\underline{\underline{\mathfrak{\sf{Explanation:-}}}}}$.

Let, m' and m" are masses of two bodies , and x , is distance between of these ......

So,

$\large\boxed{\:F'\:\:=\frac{G×m'×m"}{x^2}}$

Now,

If distance between two bodies replace in 2x ,

So, Now, Take Distance 2x in place of x .

So, Attraction force will be ,

$\large\boxed{\:F"\:\:=\frac{G×m'×m"}{(2x)^2}}$

$\implies\:F"\:\:=\frac{Gm'm"}{4x^2}$

$\implies\:F"\:\:=\:(\frac{1}{4})\:\frac{Gm'm"}{x^2}$

We know, by equation (1)

$\implies\:F"\:\:=\:F'\:×\frac{1}{4}$

$\implies\boxed{\:F"\:\:=\:0.25F'}$

So,

• When distance between two bodies = 2x , Then attraction force will be = 0.25 time of first attraction force .

________________________

Answer 2

Given to us according to question is

• Let m1 and m2 be the masses of two bodies
• The distance between them is x
• The given force of attraction is 20N
• We need to find the force of attraction at distance 2x
• We know the formula of it is F=G m1*m2/ x²
• As distance given is 2x
• Therefore put in the formula
• F= G m1*m2/ (2x)²
• F=G m1*m2/ 4x²
• Which can be written as F=0.25F'