Final answer:
To find the time it takes for the tug to rotate the asteroid's axis of rotation, we can use the equation Δt = (Δθ * I) / τ. However, since we don't have the moment of inertia of the asteroid, we cannot calculate the exact time.
Step-by-step explanation:
To find the time it takes for the tug to rotate the asteroid's axis of rotation through an angle of 10.0 degrees, we can use the equation:
Δθ = τ * Δt / I
Where Δθ is the angle of rotation (10.0 degrees or 0.1745 radians), τ is the torque applied by the tug (265 N), Δt is the time, and I is the moment of inertia of the asteroid.
Rearranging the equation, we have:
Δt = (Δθ * I) / τ
Substituting the values, Δt = (0.1745 * I) / 265.
Since we don't have the moment of inertia of the asteroid, we cannot calculate the exact time. Therefore, we cannot determine which option (a, b, c, or d) is the correct answer.