One end of an iron chain is fixed to a sphere of mass M = 10 kg and of diameter D = 0.3 m (the volume of such a sphere is `V = 0.0141 m^(3)`), while the other end is free. The length 1 of the chain is 3 m and its mass m is 9 kg. The sphere with the chain is in a reservoir whose depth `H = 3m`.
Determine the depth at which the sphere will float, assuming that iron is 7.85 times heavier than water.

One end of a long iron chain of linear mass density lambda is fixed to a sphere of mass m and specific density 1/3 while the other end is free. The sphere along with the chain is immersed in a deep lake. If specific density of iron is 7 , the height h above the bed of the lake at which the sphere will float in equilibrium is (assume that the part of the chain lying on the bottom of the lake exerts negligible force on the upper part of the the chain)

A sphere of mass 10 kg and radius 0.5 m rotates about a tangent. The moment of inertia of the sphere is

A sphere of mass 5kg and diameter 2 m rotates about a tangent. What is its moment of inertia in kg m^(2) ?

What is the moment of Inertia of a sphere of mass 20 kg and radius 1/4 m about its diameter ?

A chain of length l and mass m lies on the surface of a smooth sphere of radius R>l with one end tied to the top of the sphere.