A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L  and height h.  What is the speed of its centre  of mass when the cylinder reaches its bottom?

Angular momentum  :

Three identical metal balls each of radius r  replaced touching each other on a horizontal surface such that an equilateral triangle is formed with centers of three balls joined.  The centre of mass of the system is located at ______.

A ring of mass m and radius r rotates about an axis passing through its center and perpendicular to its plane with angular velocity on its kinetic energy is _______

A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the centre of mass

A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is

The angular momentum of a body with mass ( m) moment of inertia ( I ) and angular velocity  ( ω ) rad/s  is equal to ____.

In a rectangle ABCD ( BC = 2AB). Through which axis the moment of inertia is minimum
   

A solid sphere, disc and solid cylinder, all of the same mass and made of same material are allowed to roll down ( from rest ) on the inclined plane, then :

ABC is a right angled triangular plate of uniform  thickness.  The sides are such that AB >  BC  as shown in figure. I₁ , I₂, I₃ are  moments of inertia about AB, BC  and AC respectively.  Then which of the following relations is correct ?