Question

Two planets a and b of mass 4m and m, and radius 2r and r have their centres at

Answer 1

the center of these circles are at the end of their radius

Answer 2

Answer:

The two planets have their centers at $\frac{9r}{5}$

Explanation:

Here we have been mentioned that the two planets a and b respectively have masses 4m and m. Their radii are 2r and r respectively.

To find the position of their center or the center of mass we will use the following formula:

Let R be the position of the center of mass of the two respective planets:

Now we have,

$m_{1} = 4m$

$m_{2} = m$

$r_{1} = 2r$

$r_{1} = r$

The formula for finding the center of mass of the two planets:

$(m_{1} +m_{2} ) R = m_{1} r_{1} + m_{2} r_{2}$

⇒ $R = \frac{m_{1} r_{1} +m_{2} r_{2} }{m_{1}+m_{2}}$

⇒ R = $\frac{4m(2r) + m(r)}{4m +m}$

⇒ R = $\frac{8mr + mr}{5m}$

⇒ R = $\frac{9mr}{5m}$

⇒ R = $\frac{9r}{5}$

Therefore the center or the center of mass is at $\frac{9r}{5}$