Question

Two planets of radii r1, andr2, are made
from the same material. Two ratio of the
acceleration of gravity g1/g2, at the
surface of the planets is
1) r1/r2
2) r2/r1
3) (r1/r2)^2
4) (r2/r1)^2​

Answer 1

Answer is  in the image given below

Answer 2

Answer:

$\large \implies \sf \dfrac {r_1}{r_2}$

Solution:

We know that,

Acceleration due to gravity, $\sf g = \dfrac {Gm}{R^2}$

Mass of planet, $\sf (m_1) = density \times volume.$

$\implies \sf d \times \dfrac {4}{3} \pi r_1^3$

$\implies \sf m_2 = d \times \dfrac {4}{3} \pi r_2^3$

Now,

$\implies \sf g_1 = \dfrac {4 (G \times d \times \pi r_1^3)}{3r_1^2}$

$\implies \sf g_1 = \dfrac {4}{3} G \times d \times r_1$

$\implies \sf g_2 = \dfrac {4 (G \times d \times \pi r_2^3)}{3 r_2^2}$

$\implies \sf g_2 = \dfrac {4}{3} G \times d \times r_2$

Now,

To find the ratio of acceleration due to gravity = ?

So,

$\implies \sf \dfrac {g_1}{g_2}$

$\implies \sf \dfrac {g_1}{g_2} = \dfrac {\dfrac {4}{3} \times G \times d \times r_1}{\dfrac {4}{3} \times G \times d \times r_2}$

$\implies {\red{\sf \dfrac {g_1}{g_2} = \dfrac {r_1}{r_2}}}$