A thin uniform rod of mass $M$ and length $L$ is bent into a semicircle. A particle of mass $m$ is placed at the center of the semicircle. The gravitational force exerted by the rod on the particle is:

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 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:

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is

Two spheres of masses $1\,kg$ and $4\,kg$ are connected by a rigid, massless rod of length $10\,m$. Determine the position of the centre of mass of this system with respect to the $1\,kg$ sphere.

A thin uniform disc of mass $M$ and radius $R$ has a small hole of radius $r$ drilled at a distance $d$ from its center. The moment of inertia of the remaining portion about an axis passing through the center of the original disc and perpendicular to its plane is:

The center of mass of a system of particles depends on:

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

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

Four particles of masses m,2m,3m and 4m are arranged at the corners of a parallelogram with each inside equal to a and one of the angle between two adjacent sides is ${60^0}$. The parallelogram lies in the x-y plane with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at

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?