State the expression for moment of inertial of the following (1)A rod (2) Rectangular plate (3) ring (4) circular disc

To find the expressions for the moment of inertia of various objects, we need to consider their respective shapes and dimensions. Here are the expressions for the moment of inertia for the objects you mentioned:

(1) A rod:
The moment of inertia of a rod depends on its length (L) and mass (M) and is given by the formula: I = (1/12) * M * L^2

(2) Rectangular plate:
The moment of inertia of a rectangular plate depends on its length (L), width (W), and mass (M), assuming the plate is uniform and of negligible thickness. The formula for calculating its moment of inertia about an axis perpendicular to the plate and passing through its center of mass is: I = (1/12) * M * (L^2 + W^2)

(3) Ring:
For a thin, hollow ring with mass M and radius R, the moment of inertia can be calculated using the formula: I = M * R^2

(4) Circular disc:
The moment of inertia of a circular disc depends on its mass (M) and radius (R) and is given by: I = (1/2) * M * R^2

These formulas provide the expressions for the moment of inertia for each of the mentioned objects. Keep in mind that these formulas assume uniform distribution of mass for these objects.