Question

The force between the two masses separated by a distance ‘d’ are given in Fig (i). What change will you observe in the cases shown in fig(ii) and fig(iii)

Answer 1

Given:

The force between the two masses separated by a distance ‘d’ are given in Fig (i).

To find:

What changes will be observed in fig (ii) and (iii)?

Solution:

First of all, latest calculate the gravitational force of attraction between the masses in all the three cases:

Case 1: (when distance is d)

$\sf \therefore \: F = G \dfrac{Mm}{ {d}^{2} }$

Case 2: (when distance is d/2)

$\sf \therefore \: F_{2} = G \dfrac{Mm}{ {( \frac{d}{2}) }^{2} }$

$\sf \implies\: F_{2} = 4 \times G \dfrac{Mm}{ {d }^{2} }$

$\sf \implies\: F_{2} = 4 \times F$

So, force becomes 4 times the initial force.

Case 3: (when distance is 3d)

$\sf \therefore \: F_{3} = G \dfrac{Mm}{ {(3d) }^{2} }$

$\sf \implies\: F_{3} = G \dfrac{Mm}{ 9{d}^{2} }$

$\sf \implies\: F_{3} = \dfrac{1}{9} \times G \dfrac{Mm}{ {d}^{2} }$

$\sf \implies\: F_{3} = \dfrac{1}{9} \times F$

So, force becomes ⅑ times the initial force.

Hope It Helps.