Q, A cylindrical portion of radius r is removed from a solid sphere of radius R and uniform volume

A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . They y -coordinate of the centre of mass of the remaining sphere is

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

The radius of gyration of a solid sphere of radius R about its tangent is

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure Taking gravitational potential V =0at r = oo, the potential at (G = gravitational constatn)

There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portional is M. What is the gravitational potential at centre?

A non-conducting sphere of radius R has a spherical cavity of radius R//2 as shown. The solid part of the sphere has a uniform volume charge density rho . Find the magnitude and direction of electric field at point (a) O and (b) A.

A uniform disc of mass m & radius R is pivoted at its centre O with its plane vertical as shown in figure A circular portion of disc of radius (R )/(2) is removed from it. The time period of small oscillations of remaining portion about O is -

A uniform disc of mass m & radius R is pivoted at its centre O with its plane vertical as shown in figure A circular portion of disc of radius (R)/(2) is removed from it. Then choose the correct option(s)

A sphere of maximum volume is cut out from a solid hemisphere of radius r . The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3 : 2 (b) 4 : 1 (c) 4 : 3 (d) 7 : 4

An infinity long cylinder of radius R has an infinitely long cylindrical cavity of radius (R)/(2) are shown in the figure. The remaining portion has uniform volume charge density rho . The magnitude of electrical field at the centre of the cavity is-