Question

the mass of the earth is 6.0×10^24 kg calculate (1) the potential energy of a body of mass 33.5 kg and (2) the gravitational potential. at a distance at a distance of 3.35×10^10 m from the center of the earth take G=6.67×10^-11 Nm^2 kg^-2 sl arrora book

Answer 1

Answer : (1) 3028.5

               (2) 9.204

Answer 2

Given :

Mass of earth , $M=6\times 10^{24\ }\ kg$ .

Mass of body , m = 33.5 kg .

Gravitation constant , $G=6.67\times 10^{-11}\ N\ m^2\ kg^{-2}$ .

Distance between earth and body , $R=3.35\times 10^{10}\ m$ .

To Find :

(1) The potential energy of a body of mass 33.5 kg .

(2) The gravitational potential of given distance  .

Solution :

a )

Potential energy is given by :

$P.E=\dfrac{GMm}{R^2}\\\\P.E=\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}\times 33.5}{(3.35\times 10^{10})^2}\\\\P.E=1.2\times 10^{-5}\ J$

b )

Gravitation potential at distance R is given by :

$P=\dfrac{GM}{R^2}\\\\P=\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}}{(3.35\times 10^{10})^2}\\\\P=3.56\times 10^{-7}\ J\ kg^{-1}$

Hence , this is the required solution .