Two particles of masses $m_1$ and $m_2$ are connected by a massless rigid rod of length $L$. The system rotates with a constant angular velocity $\omega$ about an axis perpendicular to the rod and passing through its center of mass. The kinetic energy of the system is:

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

A system consists of three particles of masses 1 kg, 2 kg, and 3 kg located at the vertices of an equilateral triangle of side 'a'. The distance of the center of mass from the 1 kg mass is:

A uniform rod of negligible mass and length $4\,m$ has point masses of $2\,kg$ and $6\,kg$ fixed at its ends. Find the distance of the centre of mass from the $2\,kg$ mass.

In the HCl molecule, the separation between the nuclei of the two atoms is about $1.27\;{A^0}\;\left( {1{A^0}\; = {{10}^{ - 10}}m} \right)$. The approximate location of the centre of mass of the molecule, assuming the chlorine atom to be about 35.5 times massive as hydrogen is

Two particles of mass ${\rm{5}}\,\,{\rm{kg}}$ and ${\rm{10}}\,\,{\rm{kg}}$ respectively are attached to the two ends of a rigid rod of length ${\rm{1}}\,{\rm{m}}$ with negligible mass. The centre of mass of the system from the ${\rm{5}}\,\,{\rm{kg}}$ particle is nearly at a distance of:

A loded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation $heta$. The gun was initially at rest on a horizontal frictionless surface. After firing, the centre of mass of gun-shot system

If two particles of masses $3\,\,kg$ and $6\,\,kg$ which are at rest are separated by a distance of $15\,\,m.$. The two particles are moving towards each other under a mutual force of attraction. Then the ratio of distances travelled by the particles before collision is

If two particles of masses $3\,\,kg$ and $6\,\,kg$ which are at rest are separated by a distance of $15\,\,m.$. The two particles are moving towards each other under a mutual force of attraction. Then the ratio of distances travelled by the particles before collision is

The distance b/w the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1{A^0}$. Given mass of carbon atom is 12.a.m.u., and mass of oxygen atom is 16.a.m.u., calculate the position of the centre of mass of the carbon monoxide molecule

Two particles of masses 4 kg and 6 kg are separated by a distance of 20 m and are moving towards each other under mutual force of attraction, the position of the point where they meet is