Class 11 System of Particle test Written

 

The moment of inertia of a semicircular ring of mass M and radius R about an axis which is passing through its centre and at an angle θ with line joining its ends as shown in figure is

 

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is Class 11 Rotational Motion

 

A carpet of mass M made of in-extensible material is rolled along its length in the form of a cylinder of radius R and kept along a rough floor. The carpet starts unrolling without sliding on the floor, when a negligibly sniall push is given to it. The horizontal velocity of, the axis of a cylindrical part of the carpet when its radius is reduced to R/2 is

Ans:  sqrt(14/3 gr)