Final answer:
a) The moment of inertia of the sphere is 0.002162 kg*m^2. b) The gravitational potential energy is 0. c) The angular momentum cannot be calculated without additional information. d) The surface area of the sphere is 0.022 m^2.
Step-by-step explanation:
a) To calculate the moment of inertia of the sphere, we can use the formula for the moment of inertia of a solid sphere:
I = (2/5) * m * r^2
where I is the moment of inertia, m is the mass of the sphere, and r is the radius of the sphere.
Plugging in the values: I = (2/5) * 0.85 kg * (0.042 m)^2 = 0.002162 kg*m^2
b) The gravitational potential energy of the sphere can be calculated using the formula:
PE = m * g * h
where PE is the gravitational potential energy, m is the mass of the sphere, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the sphere.
As the sphere is not lifted or moved vertically, the height h is 0. Therefore, the gravitational potential energy is 0.
c) The angular momentum about a given axis can be calculated using the formula:
L = I * ω
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
However, the angular momentum about a given axis is not provided in the question, so an answer cannot be calculated without additional information.
d) The surface area of the sphere can be calculated using the formula:
A = 4 * π * r^2
where A is the surface area of the sphere and r is the radius of the sphere.
Plugging in the values: A = 4 * π * (0.042 m)^2 = 0.022 m^2