Three identical spheres each of mass M are pl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the positions of the three spheres be $(0, 0)$,$(3, 0)$,and $(0, 3)$ in meters.The mass of each sphere is $M$.The position vector of the centr

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) Let the positions of the three spheres be $(0, 0)$,$(3, 0)$,and $(0, 3)$ in meters.The mass of each sphere is $M$.The position vector of the centre of mass $\overrightarrow{r}_{	ext{com}}$ is given by:$\overrightarrow{r}_{	ext{com}} = \frac{M(0\hat{i} + 0\hat{j}) + M(3\hat{i} + 0\hat{j}) + M(0\hat{i} + 3\hat{j})}{M + M + M}$$\overrightarrow{r}_{	ext{com}} = \frac{M(3\hat{i} + 3\hat{j})}{3M} = \frac{3\hat{i} + 3\hat{j}}{3} = \hat{i} + \hat{j}$The magnitude of the position vector is:$|\overrightarrow{r}_{	ext{com}}| = \sqrt{1^2 + 1^2} = \sqrt{2}$Given that the magnitude is $\sqrt{x}$,we have $\sqrt{x} = \sqrt{2}$,which implies $x = 2$.

Similar Questions

Obtain the general expression for the centre of mass of a system of $n$ distributed particles in three dimensions.

Masses $m, (1/2)(m/2), (1/2)^2(m/3), \dots, (1/2)^{N-1}(m/N), \dots \infty$ 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:

Particles of masses $m, 2m, 3m, \ldots, nm$ grams are placed on the same line at distances $l, 2l, 3l, \ldots, nl$ cm from a fixed point. The distance of the centre of mass of the particles from the fixed point in centimetres is:

In an $HCl$ molecule,the distance between the nuclei of the two atoms is $1.27 \ \mathring A$. The $Cl$ atom is approximately $35.5$ times heavier than the $H$ atom. The center of mass of this molecule will be at a distance of approximately ....... $\mathring A$ from the center of the $H$ atom.

Vedclass Test Series

Exam Paper Generator

Online Exam Module