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Solution :
We know that :
Formula for Gravitational force is given by :

where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :

where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,



Hence derived.
Answer:
a) Left to right
b) 1.51 A
Explanation:
a)
The gravitational force on the rod due to its mass is in downward direction. hence to levitate the rod, the magnetic force on the rod must be in upward direction.
The magnetic field is inward to page and magnetic force must be upward. Using right hand rule, the current must be flowing from left to right.
Left to right
b)
L = length of the copper rod = 0.570 m
m = mass of the rod = 0.059 kg
B = magnitude of magnetic field in the region = 0.670 T
θ = Angle between the magnetic field and rod = 90
i = current flowing throw the rod = ?
The magnetic force on the rod balances the gravitational force on the rod. hence
Magnetic force = gravitational force
mg = i B L Sinθ
(0.059) (9.8) = i (0.670) (0.570) Sin90
i = 1.51 A