The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its centre on $x$ axis at a distance a from the origin. then the moment of inertia of the disc about the $x-$ axis is
$M\left( {\frac{{{R^2}}}{2}} \right)$
$M\left( {\frac{{{R^2}}}{4}} \right)$
$M\left( {\frac{{{R^2}}}{4} + {a^2}} \right)$
$M\left( {\frac{{{R^2}}}{2} + {a^2}} \right)$
Two particles having mass $'M'$ and $'m'$ are moving in circular paths having radii $R$ and $ r.$ If their time periods are same then the ratio of their angular velocities will
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ $times$ that of the cone, the position of the centre of mass of the toy is given by
The moment of inertia of a sphere (mass $M$ and radius $R$) about it’s diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $XX'$ will be
A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega .$ Two objects, each of mass $m,$ are attached gently to the opposite ends of a diameter of the ring. The ring rotates now with an angular velocity
A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$