Three particles of masses m₁= 1kg, m₂ = 2kg and m₃ = 3kg are placed at the comers of an equilateral triangle of side 1m as shown in Figure. Find the position of center of mass.

From a complete ring of mass M and radius R, a sector angle \(\theta\) is removed. What is the moment of inertia of the incomplete ring about axis passing through the center of the ring and perpendicular to the plane of the ring?

If energy of 1000 J is spent in increasing the speed of a flywheel from 30 rpm to 720 rpm, find the moment of inertia of the wheel.

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect goes from A to point B along its diameter as shown in Figure. Discuss how the angular speed of the circular disc changes?

Consider a thin uniform circular ring rolling down in an inclined plane without slipping. Compute the linear acceleration along the inclined plane if the angle of inclination is \(45 ^{0}\).