Question

The force of attraction between two bodies at a
certain separation is 10 N. What will be the force
of attraction between them if the separation is
reduced to half ?
please tell me the answer????????????​

Answer 1

The force of attraction between two bodies kept at a distance r is given by:

$\boxed{\tt F = G \dfrac{Mm}{r^2}}$

Given :

• F = 10 N

Long method :

The force of attraction when the distance is reduced to half is given by :

$\tt F' = G \dfrac{Mm}{\left(\dfrac{r}{2}\right) ^2}$

$\tt F' = G \dfrac{Mm}{\dfrac{r^2}{4}}$

$\tt F' = G \dfrac{Mm}{r^2} \times 4$

$\boxed{\tt F' = 4\ F}$

F' = 4 × 10

F' = 40 N

Short method :

Since , the force of attraction is inversely proportional to square of distance , half the distance will cause the force to become 4 times .

$\boxed{ \because \tt force \propto \dfrac{1}{ {r}^{2}}} \\ \\ \tt force = k {r}^{2} \\ \\ \tt force = k \frac{1} { {2}^{2} } \\ \\ \tt force = \frac{k}{4} \\ \\ \tt 4 \: force = k \\ \\ \underline{\sf \therefore force \: will \: become \: four \: times.}$