Question

The value of acceleration due to gravity, of a planet having mass and radius double of earth is
1 point
9.8
19.6
4.9
None of above​

Answer 1

Required Answer:

4.9 m/s^2.

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Given:

• A planet have mass and radius double of earth.

To calculate:

• Acceleration due to gravity on that planet. (g)

Calculation:

Let us assume the mass and radius of the Earth as 'm' and 'R'.

Therefore,

• The mass of the planet = 2m

• The radius of the planet = 2R

Now, we know that :-

$\sf { \leadsto g = \dfrac{Gm}{{R}^{2}}}$

Thus,

$\sf { \longrightarrow {g}_{planet} = \dfrac{G \times 2m}{{(2R)}^{2}}}$

$\sf { \longrightarrow {g}_{planet} = \dfrac{2Gm}{4{R}^{2}}}$

$\sf { \longrightarrow {g}_{planet} = \dfrac{1Gm}{2{R}^{2}}}$

Now, as we know that value of 'g' that is equal to Gm/r^2 on earth is 9.8 m/s^2. So,

$\sf { \longrightarrow {g}_{planet} = \dfrac{1}{2} \times 9.8}$

$\sf { \longrightarrow {g}_{planet} = \dfrac{9.8}{2} }$

$\sf { \longrightarrow {g}_{planet} = 4.9 \: m/{s} ^{2} }$

Thus, option C is correct.

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Answer 2

$\huge\underline{\bf \orange{AnSweR :}}$

Now, we know that :-

g= Gm/R²

Thus,

g planet = G×2m/(2R)²

g planet = 2Gm/4R²

g planet = 1Gm/2R²

Now, as we know that value of 'g' that is equal to Gm/r² on earth is 9.8 m/s².

So,

g planet = 1/2 ×9.8

g planet = 9.8/2

g planet =4.9m/s²

Thus, option C is correct.