The density of a planet is three times that of earth and radius 2.5 times that of earth. If g_p and g_e represents acceleration due to gravity on planet and earth respectively then ratio g_p to g_e is

Step-by-step solution

The acceleration due to gravity on the surface of a planet is given by g = GM R^2 Substituting the mass of the planet M = 4 3 R^3 , we get g = G R^2 ( 4 3 R^3 ) = 4 3 G R This implies that g R . The ratio of acceleration due to gravity on the planet to that on Earth is g_p g_e = R_p _p R_e _e Given that _p = 3 _e and R_p = 2.5R_e , substituting these values yields g_p g_e = (2.5) (3) = 7.5 Answer: 7.5