There is a planet which is 8 times massive and 27 times denser than the earth. If g^ and g are the accelerations due to gravity on the surfaces of the planet and the earth respectively then

Step-by-step solution

Let, d= Density of planet, aligned & M= Mass of planet & R= Radius of planet aligned then density, d= Mass Volume array ll & d= M ( 4 3 R^3 ) & R^3= 3 M 4 d array R= ( 3 M 4 d )^ 1 3 ...(i) Now, acceleration due to gravity g is given by g= G M R^2 Substituting R from Eq. (i) we get, g= G M R^2 = G M ( 3 4 M d )^ 2 3 g M^ 1 3 d^ 2 3 Hence, ratio of acceleration due to gravity on surface of planet and that on surface of earth will be g^ g = (M)^ 1 3 M^ 1 3 (d)^ 2 3 (d)^ 2 3 = ( M^ M )^ 1 3 ( d^ d )^ 2 3 Given, M^ M =