(B) Let the position of point $P$ be at the origin $(0, 0)$.Since the spheres are identical and arranged along the $X$-axis,the positions of the cente

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(B) Let the position of point $P$ be at the origin $(0, 0)$.Since the spheres are identical and arranged along the $X$-axis,the positions of the centers of mass are $P = 0$,$Q = PQ$,and $R = PR$.The mass of each sphere is $m = 1 \ kg$.The center of mass $x_{cm}$ of the system is given by:$x_{cm} = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3}$$x_{cm} = \frac{(1 \times 0) + (1 \times PQ) + (1 \times PR)}{1 + 1 + 1}$$x_{cm} = \frac{PQ + PR}{3}$

Class 11 Physics System of Particles and Rotational Motion Centre of mass (Point Mass)

Medium

Three identical spheres,each of mass $1 \ kg$,are arranged as shown in the figure. If their centers of mass are at $P$,$Q$,and $R$ respectively,what is the distance of the center of mass of this system from point $P$?

A
$\frac{PQ + PR + QR}{3}$
B
$\frac{PQ + PR}{3}$
C
$\frac{PQ + QR}{3}$
D
$\frac{PR + QR}{3}$

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System of Particles and Rotational Motion

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Centre of mass (Point Mass)

In carbon monoxide molecules,the carbon and the oxygen atoms are separated by a distance of $1.2 \,\mathring{A}$. The distance of the centre of mass from the carbon atom is ........ $\mathring{A}$.

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$A$ $T$-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 $C$.

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The variation of density of a solid cylindrical rod of cross-sectional area $\alpha$ and length $L$ is given by $\rho = \rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from that end $(x=0)$ is:

MediumWBJEE 2025

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Three identical spheres,each of mass $1 \ kg$,are kept as shown in the figure,touching each other,with their centres on a straight line. If their centres are marked $P, Q, R$ respectively,the distance of the centre of mass of the system from $P$ is

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Three particles of masses $50\, g$,$100\, g$,and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

DifficultJEE MAIN 2019

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Three identical spheres,each of mass $1 \ kg$,are arranged as shown in the figure. If their centers of mass are at $P$,$Q$,and $R$ respectively,what is the distance of the center of mass of this system from point $P$?

Similar Questions

In carbon monoxide molecules,the carbon and the oxygen atoms are separated by a distance of $1.2 \,\mathring{A}$. The distance of the centre of mass from the carbon atom is ........ $\mathring{A}$.

$A$ $T$-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 $C$.

The variation of density of a solid cylindrical rod of cross-sectional area $\alpha$ and length $L$ is given by $\rho = \rho_0 \frac{x^2}{L^2}$, where $x$ is the distance from one end of the rod. The position of its centre of mass from that end $(x=0)$ is:

Three identical spheres,each of mass $1 \ kg$,are kept as shown in the figure,touching each other,with their centres on a straight line. If their centres are marked $P, Q, R$ respectively,the distance of the centre of mass of the system from $P$ is

Three particles of masses $50\, g$,$100\, g$,and $150\, g$ are placed at the vertices of an equilateral triangle of side $1\, m$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be

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