The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $X$-axis is

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

The ratio of the radius of gyration of a ring to that of a disc (both circular) of the same radius and mass,about a tangential axis perpendicular to the plane is

$A$ circular disc is made using iron and aluminum. To maximize the moment of inertia about its geometric axis,which configuration is preferred?

The densities of two solid spheres $A$ and $B$ of the same radii $R$ vary with radial distance $r$ as $\rho_A(r) = k \left(\frac{r}{R}\right)$ and $\rho_B(r) = k \left(\frac{r}{R}\right)^5$,respectively,where $k$ is a constant. The moments of inertia of the individual spheres about axes passing through their centres are $I_A$ and $I_B$,respectively. If $\frac{I_B}{I_A} = \frac{n}{10}$,the value of $n$ is

We have two spheres,one solid and one hollow. Their moments of inertia about their respective diameters are equal. The ratio of their radii will be: