A floor-mat of mass M made up of extensible material, is rolled along its length so as to form a cylinder of radius R and kept on a rough horizontal surface. If the mat is now unrolled, without sliding, to a radius `(R )/(2)`, the decrease in potential energy is

A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a graph floor. The carpet. Starts unrolling without sliding on the floor when a negligible small push is given to it. Calculate the horizontal velcoity of the axis of the cylindrical part of the carpet when its radius reduces to R//2 .

A carpet of mass M is rolled along its length so as to from a cylinder of radius R and is kept on a rough floor. When a negligibly small push is given to the cylindrical carpet, it stars unrolling itself without sliding on the floor. Calculate horizontal velocity of cylindrical part of the carpet when its radius reduces to R//2 .

A carpet of mass M is rolled along its length so as to from a cylinder of radius R and is kept on a rough floor. When a negligibly small push is given to the cylindrical carpet, it stars unrolling itself without sliding on the floor. Calculate horizontal velocity of cylindrical part of the carpet when its radius reduces to R//2 .

A force (F=Mg) is applied on the top of a circular ring of mass M and radius R kept on a rough horizontal surface. If the ring rolls without slipping, then minimum coefficient of friction required is