Question

if 2 planets have equal masses and their radii are R1 and 2R.calculate the ratio of accerlation due to gravity?

Answer 1

Acceleration due to gravity is given by
g = GM/R²
where , M denotes mass of planet and R denotes the radius of that planet.

case 1 :- mass = M and radius = R₁
g₁ = GM/R₁²

Case 2 :- mass = M and radius = 2R
g₂ = GM/(2R)² = GM/4R²

Now, ratio of accⁿ due to gravity = g₁/g₂
= {GM/R₁²}/{GM/4R²}
= 4R²/R₁²

Hende, ratio of accⁿ due to gravity = 4R² : R₁²

Answer 2

Hello Dear.

Here is the answer---

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Let the Mass of the Planet be m.

For First Planet,
  Mass = m.
Radius = R₁

Using the Formula,

 g = Gm/r²
g = Gm/(R₁)²


For Second Planet,

 Mass = m
Radius = 2R

Thus, g' = Gm/(2R)²
              = Gm/4R²

∴ Ratio between the acceleration due to the Gravity of the Planets are---

  g/g' = [Gm/R₁²] ÷ [Gm/4R²]
         = 4R²/R₁²


Hence, the ratio will be 4R² : R₁²


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Hope it helps.


Have a Nice Day.