Electronics and Communication Engineering - Exam Questions Papers - Discussion

4. 

Find the electric charge required on the earth and moon to balance their gravitational attraction if the charge on the earth is 12.5 times that on the moon.
Mass of moon = 6.7 x 1022 Kg
Mass of earth = 6 x 1024 Kg
Distance between moon and earth = 380 Km
Universal gravitational constant = 6.7 x 10-11 Nm2/Kg2

[A]. 48.9 TC
[B]. 4.89 GC
[C]. 4.89 TC
[D]. 48.9 GC

Answer: Option C

Explanation:

Using law of gravitations, the force between two point masses is F =

M1 = mass of moon = 6.7 x 1022 kg

M2 = mass of earth = 6 x 1024 kg

r = distance between masses = 380 km

G = universal gravitational constant

= 6.7 x 10- 11 Nm2/Kg2

Let Q1 and Q2 be the charge on moon and earth respectively. Now the gravitational force must be balanced by the force of repulsion.

Q1Q2 = 4pε0M1M2G

but Q2 = 12.5Q1

= 12.5 x 4pω0M1M2G

Q2 = 6.11 x 1014

Q2 = 61.11 TC

Q1 = 4.89 TC.


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