Question

17.If the gravitational force on body 1 due to 2 is given by F12 and on body 2 due to 1 is F21 then
(a) F12 = F21
(b) F12 = - F21
(c) F12 = F21/4
(d) none​

Answer 1

Answer:

(d )none

Explanation:

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Answer 2

Answer:

The gravitational force on body 1 due to 2 is given by F₁₂ and on body 2 due to 1 is F₂₁ then F ₁₂= - F₂₁.i.e.option (b).

Explanation:

Consider two point masses m₁ and m₂ separated by distance r. The gravitational force acting on m₁ due to m₂ is given by;

$\overrightarrow{F{_1}{_2}}=\frac{Gm_{1}m_{2}}{r^2}\hat{r_{2}_{1}}$       (1)

where,

F ₁₂=gravitational force on body 1 due to 2

m₁=mass of body 1

m₂= mass of body 2

G=universal gravitational constant

r=distance between the two bodies

Where $\hat{r_{2}_{1}}$ is the unit vector directed from m₂ to m₁.

Similarly, the force acting on m₂ due to m₁ is given by;

$\overrightarrow{F_{2}_{1}}=\frac{Gm_{1}m_{2}}{r^2}\hat{r_{1}_{2}}$         (2)

Where $\hat{r_{1}_{2}}$ is the unit vector directed from m₁ to m₂.

But,   $\hat{r_{1}_{2}}$$=-\hat{r_{2}_{1}}$   (from Newton's third law)

So, equation (2) can be written as;

$\overrightarrow{F{_2}{_1}}=-\frac{Gm_{1}m_{2}}{r^2}\hat{r_{2}_{1}}$     (3)

From equations (1) and (3) we have;

$\overrightarrow{F{_1}{_2}}=-\overrightarrow{F{_2}{_1}}$

Hence, the gravitational force on body 1 due to 2 is given by F₁₂ and on body 2 due to 1 is F₂₁ then F ₁₂= - F₂₁.i.e. option(b)