A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:
Options

Question

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:

G1 Physics · Accepted Answer

Let Earth's mass and radius be M and R. The planet has mass 2M and the same average density as Earth. Since density is proportional to M/R³: 2M/R(p)³ = M/R³ So, R(p) = 2¹ᐟ³R Surface gravity is: g = GM/R² Hence, g(p)/g(E) = [2M/M] × [R²/R(p)²] = 2/2²ᐟ³ = 2¹ᐟ³ Therefore the weight becomes 2¹ᐟ³W. Hence option A follows.