|
286. Problem 27.33 (RHK) (a) We have to find the equal amount of positive
charge that would have to be placed on the Earth and on the Moon to
neutralise their gravitational attraction. Do we have to know the Moon’s
distance from the Earth for answering this problem? (b) We have to
calculate in metric tons the amount of hydrogen that would be needed to
provide charge equal to that calculated in the part (a) of the
problem. We may use that the molar mass of hydrogen is
|
.|
Solution: Click For PDF Version We use the following data: Mass of the Earth,
mass of the Moon,
The magnitude of the force of attraction between the Earth and the Moon will be
Therefore, if
or
Therefore,
It would have been noticed that as both the gravitational force and the Coulomb force are inverse square forces, we did not need to know the distance between the Earth and the Moon for answering the part (a) of the problem. (b) We will next use the data that the mass of
As the molar mass of hydrogen is 1.008 g, the mass of
|
,
.
where
R is the distance of the Moon from the Earth. Let Q C be the
amount of positive charge which when placed on both the Earth and the Moon
would balance their gravitational attraction. By Coulomb’s law the magnitude
of the force of electrostatic repulsion will be
, we
have
protons (proton is a nucleus of hydrogen atom) is 1.008 g. The total number
of protons that will have charge of
will
be
hydrogen atoms will be