Answer:
Part a)

Part b)

Part c)
distance L is independent of the mass of the sphere
Explanation:
Part a)
As we know that rotational kinetic energy of the sphere is given as

so we will have

so we will have




Part b)
By mechanical energy conservation law we know that
Work done against gravity = initial kinetic energy of the sphere
So we will have



Part c)
by equation of energy conservation we know that

so here we can see that distance L is independent of the mass of the sphere
Capacitance is a measure of charge stored per volt.
Answer:
-4*10⁴ units.
Explanation:
As the metal rod was initially neutral (which means that it has the same quantity of positive and negative charges), after being close to the charged sphere, as charge must be conserved, the total charge of the metal rod must still remain to be zero.
So, if due to the influence of the negative charge in the sphere, the half of the road closer to the sphere has a surplus charge of +4*10⁴ units, the charge on the half of the rod farther from the sphere must be the same in magnitude but of the opposite sign, i.e., -4*10⁴ units.