Question

Compare the gravitational force on a 25

.

5 kg

mass at the surface of the Earth (with ra-

dius 6

.

4

×

10

6

m and mass 6

×

10

24

kg) with

that on the surface of the Moon

with mass

1

81

.

3

M

E

and radius 0

.

27

R

E

What is the force on the Moon?

Answer in units of N

Answer 1

We know that gravitational force

F=GMem/R^2 ...1

here G=6.67×10^(-11) , Me=6×10^24 kg, m=25.5kg

R=6.4×10^6 m

put these values in equation 1

F=6.67×10^(-11)×6×10^24×25.5/(6.4×10^6)^2

F=24.915 ×10N

F=249.15 N

Similarly for the moon

M=(1/81.3)×6×10^24=7.38×10^22 kg

R=0.27×6.4×10^6 =1.728×10^6 m

from equation 1

F'=6.67×10%(-11)×7.38×10^22×25.5/(1.728×10^6)^2

F'=420.373×10^(-1)

F'=42.04 N Answer

so

F/F' =249.15/42.04

=5.93

F=5.93 F'.