Question

The gravitational force of attraction between two objects decreases by 36% when the distance between them is increased by 4 m. Find the original distance between them.

Answer 1

Let initial force of attraction between two objects is F when distance between objects is r.

But force of attraction decreased by 36% when the distance between them is increased by 4.

e.g., final force = F - 36% F = 0.64F

We know, gravitational force is inversely proportional to square of distance between objects.
so, $\frac{F_1}{F_2}=\frac{d_2^2}{d_1^2}$

or, $\frac{F}{0.64F}=\frac{(r+4)^2}{r^2}$

or, 1/(0.8)² = (r + 4)/r

or, 1/ 0.8 = (r + 4)/r

or, r = 0.8r + 3.2

or, r = 16 m

hence, original distance between them is 16m

Answer 2

Answer:

Let initial force of attraction between two objects is F when distance between objects is r.

But force of attraction decreased by 36% when the distance between them is increased by 4.

e.g., final force = F - 36% F = 0.64F

We know, gravitational force is inversely proportional to square of distance between objects.

so, \frac{F_1}{F_2}=\frac{d_2^2}{d_1^2}

F

2

F

1

=

d

1

2

d

2

2

or, \frac{F}{0.64F}=\frac{(r+4)^2}{r^2}

0.64F

F

=

r

2

(r+4)

2

or, 1/(0.8)² = (r + 4)/r

or, 1/ 0.8 = (r + 4)/r

or, r = 0.8r + 3.2

or, r = 16 m

hence, original distance between them is 16m