Question

A rigid spherical body is spinning around an axis without any external torque. Due to a change in temperature, its volume increases by 1%. Its angular speed:

(A) Increases by 1%
(B) Decreases by 1%
(C) Decreases by 0.67%
(D) Decreases by 0.33%

Answer 1

The angular speed of a spinning rigid spherical body with increased volume due to a temperature change would decrease to conserve angular momentum. The correct answer is (C) Decreases by 0.67%.

Step-by-step explanation:

The question involves concepts of rotational motion and conservation of angular momentum in Physics. When a rigid spherical body, which is spinning around an axis without any external torque, experiences an increase in its volume due to a temperature change, the moment of inertia of the body also increases because the moment of inertia is directly related to the mass distribution of the body.

In the absence of external torque, conservation of angular momentum must be upheld, which states that the initial angular momentum (Li = Iiωi) must equal the final angular momentum (Lf = Ifωf), where I is the moment of inertia and ω is the angular speed. If increases due to the increased volume and mass distribution, then the angular speed ωf must decrease to maintain the conservation of angular momentum.

For a spherical body, the moment of inertia is proportional to its radius squared (I ≈ r²). Therefore, if the volume increases by 1%, the radius would increase by approximately (1/3)% (since volume is proportional to radius cubed). Consequently, the moment of inertia would increase by approximately (2/3)% (since the moment of inertia is proportional to radius squared). Using conservation of angular momentum and assuming mass remains constant, the decrease in angular speed would then be by approximately (2/3)%, making the correct answer (C) Decrease by 0.67%.