System of Parti...

A solid disc has a radius $$R$$. Density of its material is given by $$\rho={\rho}_{0}(2-\cfrac{r}{R})$$ where $${\rho}_{0}$$ is a constant and $$r$$ is the radial distance measured from the centre. Then the moment of inertia of the disc about an axis passing through its centre and perpendicular to the plane of the disc is 

Two circular lamina are cut from the same uniform sheet of metal and have radii in the ratio $$1:2$$. What is the ratio of their moments of inertia about their respective diameters?

Find the moment of inertia I of the system (Axis is perpendicular to the plane passing through O).

Let $$ \xrightarrow [ P ]{  }  $$ be the liner momentum of a particle whose whose position fector is $$ \xrightarrow [ r ]{  }  $$ with respect to the origin and $$ \xrightarrow [ L ]{  }  $$ be the angular momentum at this particle about the origin then.

The mass of a uniform ladder of length 5m is 20 kg. A person of mass 60 kg stand on the ladder at a height of 2m from the bottom . the position of centre of mass of the ladder and man from the bottom is 

A square sheet of edge length L and uniform mass per unit area a is used to form a hollow cylinder. The moment of inertia of this cylinder about the central axis is

Two cylinders of equal length and equal diameter, one of wood and the other of iron are placed on an inclined on an inclined plane. Which will roll down faster?

A body of mass 'm' is dropped and another body of mass M is projected vertically up with speed 'u' simultaneously from the top of the tower of height H. If the body reaches the highest point before the dropped body reaches the ground , then maximum height raised by the centre of mass of the system from ground is 

As shown in figure two uniform rods of mass m and length l are joined. What is the MOI of system above axis perpendicular to plane of figure through end A?

Two objects of masses 200 gram and 500 gram possess
velocityies $$10\mathop i\limits^ \wedge  $$m/s and $$3\mathop i\limits^ \wedge   + 5\mathop j\limits^ \wedge  $$m/s respectively. The velocity of their centre of mass
in m/s is: