Two discs of same mass and same thickness $(t)$ are made from two different materials of densities $d_1$ and $d_2$ respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of the two discs about an axis passing through the centre and perpendicular to the plane of the disc is:

Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is

$A$ circular disc is made using iron and aluminum such that its moment of inertia about its geometric axis is maximum. For this to happen:

Let the moment of inertia of a hollow cylinder of length $30\, cm$ (inner radius $r = 10\, cm$ and outer radius $R = 20\, cm$),about its axis be $I$. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $I$,is ......... $cm$.

$A$ light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

From a uniform wire,two circular loops are made: $(i)$ $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$). (in $\sqrt{2}$)