Question

planet x is twice the radius of y and its of material of same density. the ratio of acceleration due to gravity at surface of y is

Answer 1

Answer:

$g_x:g_y = 2:1$

Explanation:

Assumptions:

$R_x$ = radius of planet x.

$R_y$ = radius of planet y.

$\rho$ = density of both the planets.

The acceleration due to gravity at the surface of a planet is given by

$g = \dfrac{GM}{R^2}$.

where,

$G$ = Universal Gravitational constant.

$M$ = mass of the planet.

$R$ = radius of the planet.

The density of a planet is given by

$\rho = \dfrac{\text{mass of the planet}}{\text{volume of the planet}}=\dfrac{M}{\frac43 \pi R^3}\\\therefore M = \rho\ \dfrac 43 \pi R^3.$

Putting this value of mass in the expression of the acceleration due to gravity, we get,

$g = \dfrac{G}{R^2}\dfrac 43 \pi R^3 = \dfrac 43 G \pi R\\\Rightarrow g\propto R.$

The acceleration due to gravity on planet x is given by

$g_x = \dfrac 43 G \pi R_x$.

The acceleration due to gravity on planet y is given by

$g_y = \dfrac 43 G \pi R_y$.

Given that $R_x = 2R_y$

Therefore,

$\dfrac{g_x}{g_y} = \dfrac{\dfrac 43 G \pi R_x}{\dfrac 43 G \pi R_y}\\= \dfrac{\dfrac 43 G \pi (2R_y)}{\dfrac 43 G \pi R_y}\\=2$

$g_x:g_y = 2:1$

Answer 2

Explanation:

hope it helps you. ............