Give the location of the centre of mass of a $(i)$ sphere,$(ii)$ cylinder,$(iii)$ ring,and $(iv)$ cube,each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?
(N/A) The centre of mass $(C.M.)$ of a body with uniform mass density is located at its geometric centre.
$(i)$ For a sphere,the $C.M.$ is at its geometric centre.
$(ii)$ For a cylinder,the $C.M.$ is at its geometric centre (midpoint of the axis).
$(iii)$ For a ring,the $C.M.$ is at its geometric centre.
$(iv)$ For a cube,the $C.M.$ is at its geometric centre.
No,the centre of mass of a body does not necessarily lie inside the body. For example,in the case of a ring or a hollow sphere,the $C.M.$ lies at the geometric centre,which is in the empty space outside the material of the body.
$(i)$ For a sphere,the $C.M.$ is at its geometric centre.
$(ii)$ For a cylinder,the $C.M.$ is at its geometric centre (midpoint of the axis).
$(iii)$ For a ring,the $C.M.$ is at its geometric centre.
$(iv)$ For a cube,the $C.M.$ is at its geometric centre.
No,the centre of mass of a body does not necessarily lie inside the body. For example,in the case of a ring or a hollow sphere,the $C.M.$ lies at the geometric centre,which is in the empty space outside the material of the body.
Explore More
Similar Questions
Weights of $1\,g, 2\,g, \dots, 100\,g$ are suspended from the $1\,cm, 2\,cm, \dots, 100\,cm$ marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium?
Difficult
View Solution$A$ rod of length $L$ has non-uniform linear mass density given by $\rho(x)=a+b\left(\frac{x}{L}\right)^{2}$,where $a$ and $b$ are constants and $0 \leq x \leq L$. The value of $x$ for the centre of mass of the rod is at
DifficultJEE MAIN 2020
View SolutionMasses $m, (1/2)(m/2), (1/2)^2(m/3), \dots, (1/2)^{N-1}(m/N), \dots \infty$ are placed at $x = 1, 2, 3, \dots, N, \dots \infty$ respectively. If the total mass is $M$,then the centre of mass of the system is:
DifficultAP EAMCET 2022
View SolutionThree particles of masses $1\,kg$,$\frac{3}{2}\,kg$,and $2\,kg$ are located at the vertices of an equilateral triangle of side $a$. The $x, y$ coordinates of the centre of mass are
Medium
View SolutionConsider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the center of mass through a distance $d$,by what distance should the second particle be moved so as to keep the center of mass at the same position?
MediumAIPMT 2004
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo