If the diameter of a flywheel is increased by $1\%$,then the percentage increase in its moment of inertia about an axis passing through its center will be ....... $\%$

The wheels of moving vehicles are made hollow in the middle and thick at the rim because...

$A$ solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $(k_{\text{sph}} : k_{\text{cyl}})$ is $2 : \sqrt{x}$,then the value of $x$ is .............

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

Let $M$ and $L$ be the mass and length of a thin uniform rod,respectively. In the $1^{\text{st}}$ case,the axis of rotation passes through the center and is perpendicular to its length. In the $2^{\text{nd}}$ case,the axis of rotation passes through one end and is perpendicular to its length. The ratio of the radius of gyration in the first case to the second case is:

$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is