System of Parti...

A circular platform is mounted on a vertical frictionless axle. Its radius is  $$r = 2 { m }$$  and its moment of inertia is  $$I=200{ kg }-{ m }^{ { 2 } }.$$  It is initially at rest. A  $$70 { kg }$$  man stands on the edge of the platform and begins to walk along the edge at speed  $$v _ { 0 } = 1.0 { m } /  { s }$$  relative to the ground. The angular velocity of the platform is

A thin wire of length L and uniform linear density $$\rho$$  used to form a ring. The M.I. of this ring about tangential axis laying in its planes is:

If the radius of solid sphere is $$\frac{1}{2}\sqrt{\frac{5}{7}}$$ m, Thin its radius of gyration when the axis is along the tangent is -

The momentum of body is numerically equal to its kinetic energy,  The velocity of the body is : 

Two disc one of density $$7.2{ g/cm }^{ 3 }$$ and the other of density $$8.9{ g/cm }^{ 3 }$$ are of same mass and thickness. Their moments of inertia are in the ratio:-

Two identical particle move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of centre of mass is

A 5kg body collides with another stationary body. after the collision , the bodies moves in the same direction with one-third of the velocity of the first body . the mass of the second body will be-

Find I of the rod along the given axis. Suppose the mass of the rod is $$m$$.

From a disc of radius R, a concentric circular portion of radius r is cut out so as leave an annular disc of mass M. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its center of gravity is

A uniform rod of mass 6M and length 6I is bent to make an equilateral hexagon. If M.I. about an axis passing through the centre of mass and perpendicular to the plane of hexagon is