Question

The surface gravity on Earth is approximately 10 N/kg. What would the surface gravity be if the Earth contained twice as much mass? *​

Answer 1

Answer:

The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).[2][3]

Answer 2

Given :

• Surface of Gravity on the surface of Earth = 10 N kg¯¹.

To Find :

⠀⠀⠀⠀⠀The surface of Gravity on earth if the mass is doubled.

Solution :

To find the acceleration due to gravity on the surface of Earth when the mass is doubled , we have to find the relation between the orginal acceleration due to gravity on earth and acceleration due to gravity on earth when mass is doubled.

Let the acceleration due to gravity on earth be g.

And the acceleration due to gravity on earth when mass is doubled be g'.

Let the mass of earth be m and the radius of earth be r.

We know the Equation for acceleration due to gravity , i.e,

$\underline{\boxed{\bf{g = \dfrac{GM}{R^{2}}}}}$

Where :

• G = Universal Gravitational constant
• M = Mass of the Planet
• R = Radius of the Earth
• g = Acceleration due to gravity.

Acceleration due to gravity on earth :

Now finding the acceleration due to gravity on the planet earth (in terms of taken variables)

Using the Equation for acceleration due to gravity and substituting the values in it, we get :

$:\implies \bf{g = \dfrac{GM}{R^{2}}} \\ \\ \\ :\implies \bf{g = \dfrac{G \times m}{r^{2}}} \\ \\ \\ :\implies \bf{g = \dfrac{Gm}{r^{2}}}$

Hence, the acceleration due to gravity on the planet earth is :

$\bf{g = \dfrac{Gm}{r^{2}}}$

Acceleration due to gravity on earth when mass is doubled :

Now finding the acceleration due to gravity on the planet earth (in terms of taken variables)

Using the Equation for acceleration due to gravity and substituting the values in it, we get :

$:\implies \bf{g = \dfrac{GM}{R^{2}}} \\ \\ \\ :\implies \bf{g' = \dfrac{G \times 2 \times m}{r^{2}}} \\ \\ \\ :\implies \bf{g' = \dfrac{2Gm}{r^{2}}}$

Hence, the acceleration due to gravity on the planet earth is :

$\bf{g' = :\implies \bf{\dfrac{g'}{g}}}$

Now , dividing g' by g , we get :

$:\implies \bf{\dfrac{g'}{g}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = \dfrac{\dfrac{2Gm}{r^{2}}}{\dfrac{Gm}{r^{2}}}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = \dfrac{2Gm}{r^{2}} \times \dfrac{r^{2}}{Gm}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = \dfrac{2\not{G}\not{m}}{r^{2}} \times \dfrac{r^{2}}{\not{G}\not{m}}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = \dfrac{2}{r^{2}} \times r^{2}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = \dfrac{2}{\not{r^{2}}} \times \not{r^{2}}} \\ \\ \\ :\implies \bf{\dfrac{g'}{g} = 2} \\ \\ \\ :\implies \bf{g'= 2g}$

Hence, the relation formed is g' = 2g.

Now , putting the value of g in the equation , we get :

⠀⠀⠀⠀⠀⠀⠀⠀→⠀g' = 2g

⠀⠀⠀⠀⠀⠀⠀⠀→⠀g' = 2 × 10

⠀⠀⠀⠀⠀⠀⠀⠀→⠀g' = 20 N kg-¹

Hence, the acceleration due to gravity on the planet earth when mass is doubled is 20 N /kg.