System of Parti...

Two uniform thin rods each of mass $$'m'$$ and length $$'L'$$ are arranged to form a cross. The moment of inertia of the system about an angular bisector is

The radius of gyration of a body about an axis passing through its centre of mass is $$24\ cm$$. Calculate the radius of gyration of the body about parallel axis passing through a point at a distance $$7\ cm$$ from its centre of mass.

The radius of gyration of a body about an axis at a distance of $$4\ cm$$ from its centre of mass is $$5\ cm$$. The radius of gyration about a parallel axis through centre of mass is:

The ratio of the radii of gyration of a spherical shell and a solid sphere of the same mass and radius about a tangential axis is:

A thin rod of length $$0.6m$$ is vertically straight on the horizontal floor. This falls freely to one side without slipping of its bottom. The angular velocity of the centre of a rod when its top end touches the floor is?

Two identical discs of mass $$M$$ and radius $$R$$ are joined to form a figure of eight [see Figure]. The radius of gyration about an axis through their point of contact and perpendicular to the  plane:

A uniform rod is kept vertically on a horizontal smooth surface at a point $$O$$. If it is disturbed slightly and released, it falls down on the horizontal surface. The lower end will be

Momentum of inertia of a rod of mass $$2\ kg$$ and length $$1\ m$$ about an axis passing through a point $$25\ cm$$ from the center and normal to the length is:

A rod is placed along the line $$y=2\ x$$ with its centre at origin. The moment of inertia of the rod is maximum about

A uniform disc of mass m and radius R is projected horizontally with velocity $$v_0$$ on a rough horizontal floor, so that it starts. off with a purely sliding motion at t = 0. After $$t_0$$ seconds, it acquires a purely rolling motion as shown in figure. The velocity of the centre of mass of the disc at $$t_0$$.