The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (1 + x/L), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

Two solid spheres each of mass 2 kg and radius 75 cm are arranged as shown. Find MOI of the system about the given axis.

Two particles of masses 5 kg and 10 kg are placed along x-axis at positions x = 1 m and x = 3 m. The moment of inertia of the system about an axis respectively passing through centre of mass and parallel to y-axis is

Two circular rings (of same material) are of same thickness. The diameter of first ring is twice that of second. The moment of inertia of first ring as compared to that of second is

Moment of inertia of a system made from three uniform rods each of mass m and length l joined to each other, as shown in the figure about one end O and perpendicular to its plane will be

The momentum of inertia of a uniform thin rod about a perpendicular axis passing through on end is I1. The same rod is into a ring and its moment of inertia about a diameter is I2. If $\frac{I_1}{I_2}is\frac{X{\pi }^2}{3},$ $\frac{{}_{}}{{}_{}}\frac{{}^{}}{}$ then the value of x will be__________.