System of Parti...

The linear mass density, $$\lambda (x)$$, for a one-dimensional object of length $$2{ x }_{ 0 }$$ is plotted in the graph. The location of the center of mass for this object, from origin is $$r_0$$ then $$\frac { 9{ r }_{ 0 } }{ { x }_{ 0 } } $$ is _____

If $$I_2$$ is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and $$I_2$$ is the moment of inertia of the ring formed by the same rod about an axis tangent to the ring and perpendicular to the plane of the ring, then find the ratio $$I_1/I_2$$

An object comprises of a uniform ring of radius $$ R $$ and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following can not be the center of mass of the object?

The radius of gyration of a homogeneous solid cylinder, of length $$L$$ and radius $$R$$, for rotation about an axis perpendicular to its length through its one end is

A uniformly straight rod is placed in vertical position on a smooth horizontal surface and released. As the rod is in motion, the center of mass moves

A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of 3 $${ ms }^{ -1 }$$ and the 3 kg body has the velocity of 2 $${ ms }^{ -1 }$$. The velocity of the centre of mass of that instant is 

Two particles of masses m1 and m2 separated by a distance d are at rest initially. If they move towards each other under mutual interaction, where will they meet ?

The ratio of the radii of gyration of a circular disc and a circular ring of thr same radii about a tangential axis in the plane is:

A shell is fired from a cannon with a velocity V at an angle $$\theta$$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is.

Dozen balls kept in a box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass.