Final answer:
The correct option for the moment of inertia of a rectangular lamina about an axis passing through its centre of mass and perpendicular to its diagonal is I = m/12 * (l² + b²). Moment of inertia represents the torque needed for an angular acceleration relative to a rotational axis and is derived using I = Σmr² for complex shapes. Option number d is correct.
Step-by-step explanation:
The subject in question is the computation of the moment of inertia for a particular shape, which in this case is a rectangular lamina about an axis. The correct formula to calculate the moment of inertia for a rectangular lamina of mass m, length l, and width b about an axis passing through its centre of mass and perpendicular to its diagonal is I = m/12 * (l² + b²).
The moment of inertia is a property of a body that determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the mass distribution relative to the axis. For continuous bodies, moments of inertia can be derived through integration.
Using the definition I = Σmr², where Σ denotes the sum over all point masses in the body and r is the distance from each point mass to the axis of rotation, and utilizing integration methods over the lamina's structure, the moment of inertia can be derived for complex shapes beyond simple point masses or hoops.