The radii of 2 planets are R and 2R and their densities are P and P/2 . What is the ratio of their acceleration due to gravity at their surfaces?

The acceleration due to gravity at the surface of planet is given by:

g = (4/3)GRπρ

Now, for planet 1

R = R

ρ = P

thus,

g1 = (4/3).GRπP ...............(1)

and for planet 2

R = 2R

ρ = P/2

so,

g2 = (4/3).G.(2R).π.(P/2)

thus,

g2 = (4/3).GRπP...............(2)

so, finally we have

g1 = g2

Thus, the acceleration due to gravity of both planets will be same.So the required ratio is 1:1

  • 17

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • 7

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -6

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -4

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -3

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -7

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -9

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -1

Radius of first planet, r1 = R ; and Radius of second planet, r2 = 2R

Density of first planet, d1 = P ; and Density of second planet, d2 = P/2

Hence, their respective masses,

M1 = Volume1 x d1 and M2 = Volume2 x d2

M1 = (4/3) x x r13 x P and M2 = (4/3) x x r23 x P/2

M1 = (4/3)R3P and M2 = (2/3) x x 8R3 x P = (16/3)R3P

Let the acceleration due to gravity on the planets be g1 and g2 respectively

Hence, ratio of accelerations,

g1/g2 = (GM1/r12) / (GM2/r22)

g1/g2 = ((4/3)R3P/R2) / ((16/3)R3P/4R2)

g1/g2 = 1

Hence their acceleration due to gravity are same.

Hope you understood.... If yes, don't forget to appreciate!!!

  • -5
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