O is the centre of an equilateral triangle ABC. F₁, F₂ and F₃ are three forces acting along the side AB, BC and AC as shown in figure. What should be the magnitude of F₃. So that the total torque about O is zero ?
                            

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 :

A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis, it should be so prepared that

The moment of inertia of a disc of mass M and radius R about a tangent to its rim in its plane is  

A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its centre of mass when it reaches the bottom is _________.

A thin uniform circular ring is rolling down an inclined plane of inclination 30^o without slipping. Its linear acceleration along the inclined plane will be :

A round disc of moment of inertia I₂  about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁ rotating with an  angular velocity  ω about the same axis.  The final angular velocity of the combination of discs is _____.

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 amount of inertia of uniform circular disc of radius r  and  mass M about an axis passing from the edge of the disc and normal to the disc

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 _______