In the figure below, two point particles are fixed on an x axis separated by a d
ID: 2097392 • Letter: I
Question
In the figure below, two point particles are fixed on an x axis separated by a distance d. Particle A has mass mA and particle B has mass 5.00mA. A third particle C, of mass 75.0mA, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?
And Also. A satellite is put in a circular orbit about Earth with a radius equal to 50% of the radius of the Moon's orbit. What is its period of revolution in lunar months? (A lunar month is the period of revolution of the Moon.)
Explanation / Answer
a) gravitational forces should be equal
or GM(1)m/R(1)^2=GM(2)m/R(2)^2
or 1/x^2=5/(d-x)^2 or x=d/(1+sqrt(5))
-sqrt(5) is not taken since mass will have to lie between A and B
or x=0.309d
b)this is solved by keplers law
"The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."
ie T^2=k*r^3
or (T of satellite) =((r of satellite)/(r of moon))^(3/2)*(T of moon)
= T/ 2^1.5= 0.35355th of a lunar month
if you have doubts ..please do ask
please rate my answer