$A$ solid sphere of radius $10 \ cm$ is rotating about an axis which is at a distance $15 \ cm$ from its centre. The radius of gyration about this axis is $\sqrt{n} \ cm$. The value of $n$ is

Two discs of the same material and thickness have radii $0.2\, m$ and $0.6\, m.$ Their moments of inertia about their axes will be in the ratio

Four identical uniform solid spheres,each of same mass '$M$' and radius '$R$',are placed touching each other as shown in the figure with centers $A, B, C, D$. If $I_{A}, I_{B}, I_{C}, I_{D}$ are the moments of inertia of these spheres respectively about an axis passing through their centers and perpendicular to the plane,then:

Radius of gyration of a body depends on

Match the following columns ($R=$ radius,$k=$ radius of gyration):

Column $I$	Column $II$
$(A)$ 'k' for a solid sphere rotating about its tangent	$(P)$ $\sqrt{2}R$
$(B)$ 'k' for a ring rotating about its tangent perpendicular to its plane	$(Q)$ $\frac{R}{2}$
$(C)$ 'k' for a uniform solid right circular cone rotating about its central axis	$(R)$ $\frac{\sqrt{7}}{\sqrt{5}}R$
$(D)$ 'k' for a uniform disc rotating about its diameter	$(S)$ $\frac{\sqrt{3}}{\sqrt{10}}R$

$A$ thin disc of mass $M$ and radius $R$ has mass per unit area $\sigma (r) = kr^2$,where $r$ is the distance from its centre. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is