Question

The acceleration due to gravity g on earth's surface is 9.8 m/s. what would be the value of g for a planet whose size is the same as that of the earth but the density is twice that of earth

Answer 1

i have solved it . but u can do it yourslef just put the values , in the second picture .

Answer 2

Answer:

The value of g for a planet is 19.6 m/s².

Explanation:

Given that,

The acceleration due to gravity g on earth's surface is 9.8 m/s.

For earth,

Formula of the gravity is

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

We know that,

The density is the mass per volume.

$D = \dfrac{M}{V}$

Where, D = density

M =mass

V = volume

The mass in form of density is

$M = D\times V$

Put the value of M into the equation (I)

$g = \dfrac{GD\times V}{R^2}$....(II)

If the value of g for a planet whose size is the same as that of the earth but the density is twice that of earth

For planet,

$g' = \dfrac{G\times2D\times V}{R^2}$....(III)

The ratio of the equation (II) and (III)

$\dfrac{g}{g'}=\dfrac{ \dfrac{GD\times V}{R^2}}{\dfrac{G\times2D\times V}{R^2}}$

$\dfrac{g}{g'}=\dfrac{1}{2}$

$g'=2g$

$g' = 2\times9.8$

$g' = 19.6\ m/s^2$

Hence, The value of g for a planet is 19.6 m/s².