Moment Of Inertia Of A Rod - Practice Questions & MCQ

The moment of inertia of a uniform cylinder of length and radius about its perpendicular bisector is .  What is the ratio  such that the moment of inertia is minimum?

Four identical thin rods each of mass M and length l, form a square frame. Moment of inetia of this frame aboit an axis through the centre of the square and perpendicular to its plane is

There is a rod of length L and mass M; one line is passing through the center of the rod and another line is passing through the end of the rod; The radius of gyrations ratio of this rod for the given cases (concerning the line positions) center/end is 

A thin rod of length  is suspended from a point from on its length which is at a distance from its centre, for what value of  time period of oscillation will be minimum -
 

A thin rod of length   is suspended from a point from on its length which is at a distance from its centre, for what value of time period of oscillation will be minimum-
 

A thin rod (of mass and length ) is sliding keeping in contact with a vertical wall and a smooth surface as shown. of the rod about instantaneous axis of rotation at the instant shown is: -

A tube of length 1m is filled completely with an incompressible liquid with of mass 1kg and closed at both ends. The tube is rotated in a horizontal plane about one of its ends with a uniform angular velocity of 2rad/s. The force exerted by the liquid ath the other end is