Final answer:
The angle turned through by a disc with men walking along its rim, in the context of conservation of angular momentum, is calculated using the initial and final moments of inertia. The correct answer is B. 2mπ/(4m+M), which accounts for the mass of the men and the disc.
Step-by-step explanation:
The question involves the concept of conservation of angular momentum in the context of a horizontal circular disc with two men walking along its rim. Initially, each of the men is at rest with respect to the ground. As both men start walking in the same direction along the rim, the disc will rotate in the opposite direction (due to no external torques acting on the system) to conserve angular momentum.
For the system consisting of the two men and the disc, the total angular momentum must remain constant. The moment of inertia of the two men relative to the center of the disc changes as they move, causing a change in the angular velocity of the disc to conserve angular momentum.
The correct expression for the angle turned by the disc can be found using conservation of angular momentum:
L_initial = L_final
I_disc * ω_disc_initial + I_men * ω_men_initial = I_disc * ω_disc_final + I_men * ω_men_final
Since the ω_disc_initial and ω_men_initial are both zero (the disc and men are initially at rest), and I_disc and I_men do not change, the angular velocities are inversely proportional to the respective moments of inertia.
The correct answer is given by the expression that accounts for the initial and final moments of inertia and the fact the total angular momentum must be conserved.
Applying this principle to the possible answers and taking into account symmetry and the information provided, we find that the angle turned through by the disc with respect to the ground (in radian) is B. 2mπ/(4m+M).