Question

What would be the value of acceleration due to gravity on a planet which mass twice the mass of the earth and radius thrice the radius of earth? Take g = 9.8 m/s

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Answer 1

Required Answer:

Given:

• A planet has mass twice the mass of the earth.

• Its radius is thrice the radius of the earth.

• g = 9.8 m/s²

To calculate:

• Value of acceleration due to the gravity on that planet.

Calculation:

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

Therefore,

• Mass of the planet = 2m

• Radius of the planet = 3r

We know that,

$\sf { \longrightarrow g = \dfrac{Gm}{{r}^{2}} }$

Now,

$\sf { \longrightarrow {g}_{(Planet)} = G\dfrac{2m}{{(3r)}^{2}} }$

$\sf { \longrightarrow {g}_{(Planet)} = \dfrac{G \times 2m}{{(3r)}^{2}} }$

$\sf { \longrightarrow {g}_{(Planet)} = \dfrac{ 2Gm}{9{r}^{2}} }$

Now, as g = Gm/r² , and we are given the value of g that is 9.8 m/s². Substitute it:

$\sf { \longrightarrow {g}_{(Planet)} = \dfrac{2}{9} \times 9.8 }$

$\sf { \longrightarrow {g}_{(Planet)} = \dfrac{2 \times 9.8}{9} }$

$\sf { \longrightarrow {g}_{(Planet)} = \dfrac{19.6}{9} }$

$\sf { \longrightarrow {g}_{(Planet)} = 2.17 \: m/{s}^{2}}$

Therefore, the value of acceleration due to gravity on a planet which mass twice the mass of the earth and radius thrice the radius of earth is 2.17 m/s².

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Answer 2

We know,

g = GM/R² (relationship between ‘g’ and ‘G’)

Let, mass of Earth = M′

Radius of it = R′

∴ g′ (of Earth) = GM′/R′² = 9.8 m/s²

But it is given that,

Mass of the given planet = 2M′

Radius of the planet = 3R′

∴ g″ (of the Planet) = G(2M′)/(3R′)² = 2GM′/9R′²

⇒ g″ = 2/9 × GM′/R′² = 2/9 × g′

⇒ g″ = 2/9 × 9.8 m/s²

⇒ g″ = 2.177 m/s² {Answer}