Question

Two planets have radius in the ratio x : y and density in
the ratio m:n. The acceleration due to gravity on the
surface of the two planets will be in the ratio of​

Answer 1

Step-by-step explanation:

Hope it helps

pls mark me as brainliast ☺️

Answer 2

The ratio of acceleration due t gravity on the surface of the two planets will be xm : yn

Step-by-step explanation:

Given:

The ratio of the radius of two planets = x : y

The ratio of the densities of the planet = m : n

To find out:

The ratio of acceleration due to gravity

Solution:

We know that if the radius of a planet is R and mass M then the accleration due to gravity is given by

$g=\frac{GM}{R^2}$

if the density is d then

$M=V\times d$

$\implies M=\frac{4}{3}\pi R^3d$

Thus

$g=\frac{4}{3}\pi GRd$

If the acceleration due to gravity on the two planets is $g_1$ and $g_2$ , radii are $R_1$ and $R_2$ and densities are $d_1$ and $d_2$

Then

$\frac{R_1}{R_2}=\frac{x}{y}$

$\frac{d_1}{d_2}=\frac{m}{n}$

$g_1=\frac{4}{3}\pi GR_1d_1$

$g_2=\frac{4}{3}\pi GR_2d_2$

Therefore,

$\frac{g_1}{g_2}=\frac{R_1}{R_2}\times\frac{d_1}{d_2}$

$\implies \frac{g_1}{g_2}=\frac{xm}{yn}$

$\implies g_1:g_2=xm:yn$

Hope this answer is helpful.

Know More:

Q: Two planets have density in ratio 2:3 and radii in ratio 1:2.Then the ratio of acceleration due to gravity at their surface is :

Click Here: https://brainly.in/question/5938858