Understanding the concept of center of mass and using them to solve problems

Particles of masses are placed at the corners of a square of side L. The center of mass of the system with respect to   is__

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is from the centre of the bigger disc. The value of is__

The distance of the centre of mass of a solid uniform cone from its vertex is . If the radius of its base is R and its height is h, then is equal to_

In the HCL molecule, the separation between the nuclei of the two atoms is 1.27A°. Find the location of the center of mass of the molecule. A chlorine atom is 35.5 times heavier than a hydrogen atom.

Two bodies of masses 0.5 kg and 1 kg are lying in the X-Y plane at points -1,2 and (3,4) respectively. The center of the mass of the system is__

Two bodies of masses 10 kg and 2 kg are moving with velocities (2i-7j+3k) and (-10i+35j-3k) m/s respectively. Find the velocity of the center of the mass?

Does the center of mass of a system of two particles lie on the line joining the particles?

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and are placed on a frictionless horizontal surface. And impulse gives a speed of 14 m/s to the heavier block in the direction of the lighter block. Then, the velocity of the center of mass is__

A child is sitting at one end of a long trolley moving with a uniform speed v on a smooth horizontal floor. If the child gets up and runs on the trolley in any manner with speed u, what will be the speed of the center of mass of the system (trolley+child)?

Two particles of different masses, initially at rest, start moving towards each other under there mutual gravitational attraction. At an instant, when the speeds of the particles are v and 2v, the speed of the centre of mass is__

Three identical spheres A, B, and C each of radius R, are placed touching one another on a horizontal table. Where is the centre of mass of the system located relative to A?

Three-point masses of 1g, 2g, and 3g lie in the X-Y plane at respective points (1,2,0,-1) and (2,-3). Find the coordinates of the center of mass of the system?

The distance between the centers of carbon and oxygen atoms in the CO molecule is 0.12 nm. The distance of the center of mass of the molecule from the carbon atom is__

Do internal forces affect the motion of a system acted upon by some external force?

The location of the center of mass of a uniform triangular lamina is__