$A$ swimmer curls their body before diving into the water from a height so that:

The radius of gyration of a uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

Consider a sphere of mass $M$ and radius $R$ centered at the origin. The density of the material of the sphere is $\rho = A r^\alpha$,where $r$ is the radial distance,and $\alpha$ and $A$ are constants. If the moment of inertia of the sphere about the axis passing through the centre is $\frac{6}{7} M R^2$,then the value of $\alpha$ is

The moment of inertia $I$ of a solid sphere having fixed volume depends upon its volume $V$ as

Point masses $1, 2, 3$ and $4 \text{ kg}$ are located at the points $(0,0,0), (2,0,0), (0,3,0)$ and $(-2,-2,0)$ respectively. The moment of inertia of this system about the $x$-axis will be: (in $\text{ kg m}^2$)

$A$ flywheel is constructed such that its entire mass is concentrated at the rim because: