Define the position vector of the centre of mass.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The position vector of the centre of mass $\vec{R}$ for a system of $n$ particles with masses $m_1, m_2, ..., m_n$ located at position vectors $\vec{r}_1, \vec{r}_2, ..., \vec{r}_n$ is defined as the weighted average of the position vectors of all the particles in the system.
Mathematically,it is given by:
$\vec{R} = \frac{\sum_{i=1}^{n} m_i \vec{r}_i}{\sum_{i=1}^{n} m_i} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2 + ... + m_n \vec{r}_n}{M}$
where $M = \sum_{i=1}^{n} m_i$ is the total mass of the system.

Explore More

Similar Questions

The position of the centre of mass of a uniform semi-circular wire of radius $R$ placed in the $x-y$ plane with its centre at the origin and the line joining its ends as the $x$-axis is given by $\left(0, \frac{x R}{\pi}\right)$.
Then,the value of $|x|$ is ...... .

$A$ uniform disc of radius $R$ is placed over another uniform disc of radius $2R$ made of the same material and having the same thickness. The peripheries of the two discs touch each other. Locate the centre of mass of the system,taking the center of the large disc at the origin.

Difficult
View Solution

$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

Difficult
View Solution

$Assertion$ : The position of the centre of mass of a body depends upon the shape and size of the body.
$Reason$ : The centre of mass of a body always lies at the centre of the body.

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 \ \mathring{A}$. 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 center of mass of the carbon monoxide molecule.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo