The mean diameters of mars and earth are 6.9 ✕ 103 km and 1.3 ✕ 104 km, respectively. the mass of mars is 0.11 times earth's mass.

(a) what is the ratio of the mean density of mars to that of earth?
(b) what is the value of g on mars? m/s2
(c) what is the escape speed on mars? m/s2

(a) Ratio of mean density is 0.735

(b) Value of g on mars 0.920

(c) Escape velocity on earth is

Explanation:

We have given radius of mars and radius of earth

Mass of earth

So mass of mars

Volume of mars

So density of mars

Volume of earth  

So density of earth

(A) So the ratio of mean density

(B) Value of g on mars

g is given by

(c) Escape velocity is given by

(a) 0.72

(b) 3.83 m/s^2

(c)  5.1 Km/s

Explanation:

diameter of Mars = 6.9 x 10^3 km

Radius of Mars, Rm = 3.45 x 10^3 km = 3.45 x 10^6 m

diameter of earth = 1.3 x 10^4 km

radius of earth, Re = 6.5 x 10^3 km = 6.5 x 10^6 m

Let Me be the mass of earth.

Mass of Mars, Mm = 0.11 Me

(a) Volume of Mars, Vm = 4/3 x 3.14 x (3.45 x 10^6)³ = 1.72 x 10^20 m³

Volume of earth, Ve =  4/3 x 3.14 x (6.5 x 10^6)³ = 1.15 x 10^21 m³

density is the ratio of mass to the volume of the object.

density of mars : density of earth = 0.72

(b) The value of acceleration due to gravity

Let gm be the acceleration due to gravity on Mars

gm = 3.83 m/s^2

(c) The escape velocity is given by

escape velocity for mars = 5.1 Km/s

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.