The mass of an imaginary planet is 3 times the mass of the earth. Its diameter is 25600 km and the earth’s diameter is 12800 km. Find the value of the acceleration due to gravity at the surface of the planet. Assume g(earth) = 9.8 m/s2.
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Data : M2(planet)M1(earth)=3.
D1 (earth)=12800km
∴r1 (earth)=12800km2=6400km
=6.4×106m
D2(planet)=25600km
∴R2 (planet)=25600km2=12800km
=1.28×107m
g1(earth)=9.8m/s2,g2 (planet)=?
g=GMR2 ∴g1=GM1R21,g2=GM2R22
∴g2g1=(M2M1)(R1R2)2
∴g2=g1(M1M2)(R1R2)2
=9.8m/s2×3×(6.4×106m1.28×107m)2
=9.8×34m/s2=7.35m/s2
The acceleration due to gravity at the surface of the planet =7.35m/s2.
Explanation:
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