Question

The density of a newly discovered planet is twice that of earth . The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If the radius of earth is R, radius of planet will be

Answer 1

Let the mass of earth be M1 and that of the planet of M2.

Let the radius of the planet be R2

Volume = (4/3) ×π×r³

since density of the planet is twice that of earth,

2[M1 / {(4/3) × π × R^3}] = [ M2/ {(4/3) ×π × (R2)^3]

2[M1/R^3] = M2/(R2)^3

2 M1 / R^3 = M2 / (R2)^3

Now, mass = (G R^2)/G

( As g = ( G M) / r^2)

since g on both planets is equal,

[(2gR^2) / G] / R^3 = [( g R^2) / G] / R2^3

[( 2R^2)] / R^3 = [R2 ^2] / R2^3

2/R = 1/R2

R2 = R/2

therefore, the answer is (1/2)R

hope it helps