Consider two planets A and B. The mass of planet B is 0.012 times the mass of planet A and its radius is 0.3 times the radius of planet A. If the acceleration due to gravity at the planet A is 10 m/s2 , calculate the corresponding value at planet
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Given:
Let us consider for planet A:
mass=Mₐ
radius=Rₐ
G=gravitational constant
gₐ=10m/s²
For planet B:
mass=Mb=0.012Mₐ
radius=Rb=0.3x Ra
formula to be used:
g=GM/R²
so gₐ=GMa/Rₐ² ------(1)
gb=GMb/Rb² ----------(2)
gb/ga=(GMb/GMa) X (Ra/Rb)²
gb/ga=(0.012xMa/Ma) x (Ra/0.3 x Ra)²
gb/ga=0.012/0.3x0.3
gb/ga=0.133
gb=gaX0.133
gb=10x0.133
gb=1.33 m/s²
∴acceleration due to gravity for planet B is 1.33 m/s²
Let us consider for planet A:
mass=Mₐ
radius=Rₐ
G=gravitational constant
gₐ=10m/s²
For planet B:
mass=Mb=0.012Mₐ
radius=Rb=0.3x Ra
formula to be used:
g=GM/R²
so gₐ=GMa/Rₐ² ------(1)
gb=GMb/Rb² ----------(2)
gb/ga=(GMb/GMa) X (Ra/Rb)²
gb/ga=(0.012xMa/Ma) x (Ra/0.3 x Ra)²
gb/ga=0.012/0.3x0.3
gb/ga=0.133
gb=gaX0.133
gb=10x0.133
gb=1.33 m/s²
∴acceleration due to gravity for planet B is 1.33 m/s²
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