A hypothetical planet P is made of the same material as the Earth, so its average density is equal to that of the Earth. However, objects on the surface of P experience an acceleration due to gravity of only 4.9m/s2.
(a) Let the radius of the Earth be RE and its mass be ME. If the radius of planet P is RP, express the mass MP of planet P in terms of RP, RE, and ME.
(b) Using the information given about surface gravity, derive an expression that relates RP to RE.
(c) Hence determine the numerical values of RP and MP as fractions of RE and ME respectively.
(d) Comment briefly on whether human beings would find it easier or harder to jump on planet P as compared to the Earth, giving one quantitative reason.