Question

The distance between two bodies becomes 6 times more than the usual distance. The F becomes
A) 36 times
B) 6 times
C) 12 times
D) 1/36 times

Answer 1

Hint
Here, we will be using the formula of Newton’s Law of Gravitation which states that the gravitational force of attraction between any two particles is directly proportional to product of their masses and inversely proportional to the square of the given distance between their centres.
$F\propto \dfrac{{G{m_1}{m_2}}}{{{r^2}}}$

Complete step by step solution:
According to Newton’s law of gravitation, gravitational force F between two bodies distance r apart is $F\propto \dfrac{1}{{{r^2}}}$
Given, when the distance between the two bodies becomes 6 times than the usual distance i.e. Let new distance will be $r' = 6r$and
New force will become $F' = \dfrac{1}{{{{r'}^2}}} = \dfrac{1}{{{{\left( {6r} \right)}^2}}}$
Thus, $F' = \dfrac{1}{{36{r^2}}}$
As we can see $F\propto \dfrac{1}{{{r^2}}}$,
Putting this value in above equation, new force will be $F' = \dfrac{1}{{36}}F$
Hence, the force becomes 1/36 times the previous value.
Option (D) is correct.

Note
In these types of problems, we can solve them by simply dividing the new force with the previous value of force.
$\dfrac{{F'}}{F} = \dfrac{{\dfrac{1}{{36{r^2}}}}}{{\dfrac{1}{{{r^2}}}}}$
Cancel the ${r^2}$and simplify, we get $\dfrac{{F'}}{F} = \dfrac{1}{{36}}$
Therefore, $F' = \dfrac{1}{{36}}F$
Hence, we can see clearly that the new force becomes 1/36 times the previous value.
Trick: Also, we can solve these types of questions by a trick in which we need to find new force when there are changes in distance between two bodies. Simply, new force will be reciprocal of square of given new distance. In the above question the distance becomes 6 times therefore, taking square of 6 and reciprocal it which is 1/36. Hence the new force will become 1/36 times the previous force.