Two half lives so it is 4000 years old
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
Cm^3 is same as mL
13.5 g / 5 mL = 2.7 g/mL
look up densities of metals
aluminum has a density of 2.7 g/mL