Final answer:
a) The volume of the sphere is 310 cm^3. b) The density of the sphere is approximately 0.0027 kg/cm^3. c) The gravitational potential energy of the sphere is 0.35 J. d) The moment of inertia of the sphere is approximately 0.006 J.
Step-by-step explanation:
a) The volume of a sphere is given by the formula V = 4/3πr^3, where r is the radius. Plugging in the given radius of 4.2 cm, we can calculate the volume:
V = 4/3 * 3.14 * (4.2 cm)^3 = 310 cm^3
b) Density is defined as mass divided by volume. Given that the mass is 0.85 kg and the volume is 310 cm^3, we can calculate the density as follows:
Density = mass / volume = 0.85 kg / 310 cm^3 = 0.0027 kg/cm^3
c) The gravitational potential energy of an object near the Earth's surface is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height. Since the sphere is uniform, we can take the height as the radius. Plugging in the given values:
PE = 0.85 kg * 9.8 m/s^2 * (4.2 cm / 100) = 0.35 J
d) The moment of inertia of a solid sphere is given by the formula I = (2/5)mr^2, where m is the mass and r is the radius. Plugging in the given values:
I = (2/5) * 0.85 kg * (4.2 cm / 100)^2 = 0.006 J