System of Parti...

The moment of inertia of a body rotating about a given axis is $$12.0 kg m^2$$ in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is $$5$$cm and the unit of mass is $$10g$$?

A long slender rod of mass $$2\ kg$$ and length $$4\ m$$ is placed on a smooth horizontal table. Two particles of masses $$2\ kg$$ and $$1\ kg$$ strike the rod simultaneously and stick to the rod after collision as shown in Figure.
Velocity of the centre of mass of the rod after collision is

A string is wrapped around a cylinder of mass $$M$$ and radius $$R$$. The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string, The work done on the cylinder for reaching an angular speed $$\omega$$ is:

The radius of gyration of a ring of mass 80 g and diameter 6 cm, about an axis passing through its center of gravity and perpendicular to the plane is:

Four particles of equal masses are placed on the vertices of a square and are rotated with a uniform angular velocity about one of the edges (A) as shown in the figure. Which particle will have a larger angular momentum

The figure below shows a pattern of two fishes. Write the mapping rule for the rotation of Image A to Image B.
 

The angular momentum of a particle rotating with an angular velocity $$\omega$$ distant r from a given origin is I. If the origin is shifted by 2r, then the new angular momentum of the particle with same angular velocity will be 

Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure. Now particle A starts with a velocity $$\nu_1$$ towards line $$AB$$, particle $$B$$ starts with a velocity $$\nu_2$$ towards line $$BC$$ and particle $$C$$ starts with velocity $$\nu_3$$ towards line $$CA$$. The displacement of $$CM$$ of three particle A, B and C after time $$t$$ will be (given if $$\nu_1 = \nu_2 = \nu_3$$)

A vertical rod AC, with C at ground and A being the top most point is moving in such a way, that A moves with a speed of 8 m/s, mid point of the rod B moves with a speed of 4 m/s. along the same direction, with what velocity will the point C move

In the below example, identify the motion of the objects.