Name: Weight of an Object on Moon
Uploaded: 2019-07-19
Duration: 7 min 1 s
Description: In many space videos, astronauts are seen hopping on the surface of the moon due to their reduced weights. Watch the video to learn how to find weight on the...

Question

If a planet exists with a radius which is double that of earth and made of the same material of density

d

, find its acceleration due to gravity in terms of that on the surface of the earth.

Accepted Answer

Let $M_{e}$ be the mass of the earth, $R_{e}$ be the radius of the earth, $d$ be the density of the material of earth and $g_{e}$ be the acceleration due to gravity on the surface of the earth. We have,

$g_{e} = \frac{G M_{e}}{{(R_{e})}^{2}} . . . . . . . . . . . . . . (1)$

Where, $M_{e} = Density \times Volume$

$\Rightarrow M_{e} = d \times \frac{4}{3} \times π \times R^{3} . . . . . . . . . . . . . . (2)$ $(∵ volume of sphere is \frac{4}{3} π R^{3})$

Let $M', R', d$ and $g'$ be the mass, radius, density of material and acceleration due to gravity respectively associated with the new planet.

We have, $M' = Density \times Volume$

$\Rightarrow M' = d \times \frac{4}{3} \times π \times {(R')}^{3}$

$\Rightarrow M' = d \times \frac{4}{3} \times π \times {(2 R)}^{3}$

$\Rightarrow M' = d \times \frac{4}{3} \times π \times 8 R^{3}$

$\Rightarrow M' = 8 \times (d \times \frac{4}{3} \times π \times R^{3})$

$\Rightarrow M' = 8 M_{e} . . . . . . . . . . . . . . From equation (2)$

Therefore the acceleration due to gravity on the surface of the new planet, $g' = \frac{G M'}{R'}$

$\Rightarrow g' = \frac{G (8 M_{e})}{{(2 R_{e})}^{2}}$

$\Rightarrow g' = \frac{8 G M_{e}}{4 {(R_{e})}^{2}}$

$\Rightarrow g' = 2 \times g_{e} . . . . . . . . . . . . . . From equation (1)$

The acceleration due to gravity on the surface of the new planet will be twice the value of the acceleration due to gravity on the earth.

If a planet exists with a radius which is double that of earth and made of the same material of density $d$ , find its acceleration due to gravity in terms of that on the surface of the earth.

Important Questions on Gravitation

Learn and Prepare for any exam you want !

If a planet exists with a radius which is double that of earth and made of the same material of density d, find its acceleration due to gravity in terms of that on the surface of the earth.

Important Questions on Gravitation

Learn and Prepare for any exam you want !

If a planet exists with a radius which is double that of earth and made of the same material of density $d$ , find its acceleration due to gravity in terms of that on the surface of the earth.