Moment of inertia of a solid sphere about its diameter is $I$. It is then casted into $27$ small spheres of same diameter. The moment of inertia of each new sphere is

Two loops $A$ and $B$ of radii $R_1$ and $R_2$ are made from a uniform wire. If the moment of inertia of $A$ is $I_A$ and that of $B$ is $I_B$,then find the ratio $R_2 / R_1$ given that $I_A / I_B = 27$.

$A$ thin wire of length $L$ and uniform linear mass density $\lambda$ is bent into a circular ring. The moment of inertia of the ring about a tangential axis in its plane is:

Two rings of radius $R$ and $nR$ made of the same material have a ratio of moment of inertia about an axis passing through their centers and perpendicular to their planes as $1:8$. The value of $n$ is (mass per unit length $= \lambda$).

If the length of a thin uniform rod is $L$ and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is $K$, then $K: L=$

Two solid spheres $A$ and $B$ each of radius $R$ are made of materials of densities $\rho_A$ and $\rho_B$ respectively. Their moments of inertia about a diameter are $I_A$ and $I_B$ respectively. The value of $\frac{I_A}{I_B}$ is