System of Parti...

The radius of gyration of a disc about its axis passing through its centre and perpendicular to its plane is

A plot of angular momentum of a rigid body (along y axis) about an axis with time (along x axis) gives rise to a straight line, whose equation is given by y = 3x+1. Find the torque acting on the body

Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is then

 A ball is made of a material of density $$\rho$$ when $${ \rho  }_{ oil }<{ \rho  }<{ \rho }_{ water }$$ with $${ \rho  }_{ oil }$$ and $${ \rho  }_{ water }$$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Four particles each of mass $$'m'$$ are placed at the corners of a square of side $$'L''$$. The radius of gyration of the system about an axis normal to the square and passing through its centre.

Two identical rods each of moment of inertia $$'I'$$ about a normal axis through centre are arranged in the from of a cross. The $$M.I$$. of the system about an axis through centre and perpendicular to the plane of system is:

Moment of inertia of a uniform rod of length $$L$$ and mass $$M$$, about an axis passing through $$L/4$$ from one end and perpendicular to its length is

A small ball strikes a stationary uniform rod, which is free to rotate, in gravity-free space. The ball does not stick to the rod The rod will rotate about:

Four rods of equal length l and mass m each form a square as shown in figure. The moment of inertia of the system about the axis 1 and axis 2 is

Find the $$M.I$$. of a thin uniform rod about an axis perpendicular to tis length and passing through a point which is at a distance $$"\dfrac { l }{ 3 } "$$ from one end. Then the radius of gyration about that axis.