Due to the melting of ice at the poles of the Earth,the moment of inertia of the Earth ....,the angular velocity ....,and the duration of the day becomes ....

$A$ thin ring of mass $M$ and radius $R$ is rotating with an angular velocity $\omega$ about an axis passing through its center and perpendicular to its plane. If $4$ point masses each of mass $m$ are placed gently at the opposite ends of two mutually perpendicular diameters,what will be the new angular velocity of the system?

$A$ horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. $A$ small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduces to $60$,then the moment of inertia of the disc is .........

$A$ train is moving slowly at $2 \, m/s$ next to a railway platform. $A$ man,$1.5 \, m$ tall,alights from the train such that his feet are fixed on the ground. Taking him to be a rigid body,the instantaneous angular velocity (in $rad/s$) is

$A$ circular platform of moment of inertia $100 \ kg\ m^2$ with a boy of mass $20 \ kg$ standing at the centre completes one rotation in $10 \ s$. If he walks $2 \ m$ away from the centre along the radius,then one rotation (with respect to the ground) will be completed in $.... \ s$.

An object of mass $m$ is tied to a thin string,which is passed through a hollow tube. The tube is held in one hand and the string in the other. The object is rotated in a circle of radius $R$ with a velocity $v$. If the string is pulled downwards to decrease the radius,which of the following quantities remains conserved?