The distance between the vertex and the center of mass of a uniform solid planar circular segment of angular size `theta` and radius R is given by -

The distance of center of mass from the center of a uniform disc of radius R. if a circular plate is removed from the disc as shown in figure will be (C is centre of complete disc)

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the figure. If the center of hole is at a distance c from the center of the disc, the distance x_(2) of the center of mass of the remaining part from the initial center of mass O is given by

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the figure. If the center of hole is at a distance c from the center of the disc, the distance x_(2) of the center of mass of the remaining part from the initial center of mass O is given by

The centre of mass of a solid cone along the line form the center of the base to the vertex is at

The centre of mass of a solid cone along the line form the center of the base to the vertex is at

Find the distance of centre of mass of a uniform cone of height 'h' and base radius R, from the vertex on the line of symmetry .

The rate change of angular velocity w.r to t in uniform circular motion is a

Find the angular momentum about the axis of rotation and kinetic energy. (a) A uniform circular disc of mass m and radius R rotating about its diameter with an angular speed omega . (b) A uniform square plate of mass m and edge L rotating about its diagonal with an angular speed omega .

A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere of radius R and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is