The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is

ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. I _AB – I _BC and I _CA are the moments of inertia of the plate about AB, BC and CA as axes respectively. Which one of the following relations is correct ?
                                

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

Two bodies of mass 1 kg and 3 kg have position vectors  respectively. The centre of mass of this system has a position vector

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

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

A weightless ladder 20 ft long rests against a frictionless wall at an angle of 60^o from the horizontal. A 150 pound man is 4 ft from the top of the ladder . A horizontal force needed to keep it form slipping. Choose the correct magnitude of force from the following.?

Angular momentum  :

Two racing cars of masses m and 4m are moving in circles of radii r and 2r respectively. If their speeds are such that each makes a complete circle in the same time. Then the ratio of the angular speeds of the first to the second car is

Consider a system of two particles having masses m₁ and m₂.  If the particle of mass m₁ is pushed towards the mass centre of particles through a distance  d, by  what distance  would the particles of mass m₂ move so as to keep the mass centre of the particles at the original position?