Explanation:
It is given that,
Density of asteroid,
Mass of asteroid,
We need to find the diameter of the asteroid. The formula of density is given by:
V is the volume of spherical shaped asteroid,
r = 2441311.12 m
Diameter = 2 × radius
d = 4882622.24 m
or
Hence, this is the required solution.
(a)
The moment of inertia of a uniform-density disk is given by
where
M is the mass of the disk
R is its radius
In this problem,
M = 16 kg is the mass of the disk
R = 0.19 m is the radius
Substituting into the equation, we find
(b) 142.5 J
The rotational kinetic energy of the disk is given by
where
I is the moment of inertia
is the angular velocity
We know that the disk makes one complete rotation in T=0.2 s (so, this is the period). Therefore, its angular velocity is
And so, the rotational kinetic energy is
(c)
The rotational angular momentum of the disk is given by
where
I is the moment of inertia
is the angular velocity
Substituting the values found in the previous parts of the problem, we find