The moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod is $2400 \,g \,cm^2$. The length of the $400 \,g$ rod is nearly: (in $\,cm$)

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

If a wheel rotating with a constant angular speed experiences a break during its motion,what happens to its radius of gyration?

Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis along any one side of the triangle is:

Four point masses (each of mass $m$) are arranged in the $X-Y$ plane at coordinates $(a, 0)$,$(0, a)$,$(-a, 0)$,and $(0, 2a)$. What is the moment of inertia of this system about the $Y$-axis?

The ratio of the radius of gyration of a hollow sphere to that of a solid cylinder of equal mass,for the moment of inertia about their diameter axis $AB$ as shown in the figure,is $\sqrt{\frac{8}{x}}$. The value of $x$ is: