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:

Two objects of mass 15 kg and 25 kg respectively are connected to the two ends of a rigid rod of length 12 m with negligible mass. The distance of the center of mass of the system from the 15 kg mass is:

The distance between 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

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 the net external force on a system of particles is zero, what can be said about the velocity of the center of mass?

Three masses of 5 kg, 10 kg, and 15 kg are placed at positions x = 0 m, x = 2 m, and x = 4 m respectively along a straight line. Find the position of the center of mass of the system.

A straight rod of length L has one of its ends at the origin and the other at $x = L$. If the mass per unit length of the rod is given by $Ax$ is constant, where is its mass centre?

Masses 8,2,4,2 kg are placed at the corners A,B,C,D respectively of a square ABCD of diagonal 80 cm. The distance of centre of mass from A will be

The centre of mass of system of three particles of masses 1g, 2g, and 3g is taken as the origin of a co-ordinate system. The position vector of a fourth particle of mass 4g. Such that the centre of mass of the four particle system lies at the point (1,2,3) is $\alpha \,{\rm{(}}\widehat {\rm{i}}{\rm{ + 2}}\widehat {\rm{j}}{\rm{ + 3}}\widehat {\rm{k}}{\rm{)}}$ Where $\alpha$ is a constant. The value of '$\alpha$' is

A circular disc of radius R has a circular hole of radius R/2 cut out of it. The center of the hole is at a distance R/2 from the center of the disc. Where is the center of mass of the remaining portion?

Two particles of masses 2 kg and 3 kg are located at (1, 2) and (-1, 3) respectively. What are the coordinates of the center of mass of the system?