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?
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