Three identical spheres,each of mass 1 kg,ar | vedclass

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

Question

(B) Let the radius of each sphere be $r$. Since the spheres are identical and touching,the distance between the centres of adjacent spheres is $2r$.Le

Vedclass · Accepted Answer

$\frac{KL + KM}{3}$

Vedclass · Answer

(B) Let the radius of each sphere be $r$. Since the spheres are identical and touching,the distance between the centres of adjacent spheres is $2r$.Let the positions of the centres be $x_K = 0$,$x_L = 2r$,and $x_M = 4r$.The mass of each sphere is $m = 1 \ kg$.The centre of mass $X_{cm}$ is given by $X_{cm} = \frac{m x_K + m x_L + m x_M}{m + m + m} = \frac{0 + 2r + 4r}{3} = \frac{6r}{3} = 2r$.Since $KL = 2r$ and $KM = 4r$,we have $X_{cm} = KL = \frac{KM}{2}$.Alternatively,$X_{cm} = \frac{KL + KM}{3} = \frac{2r + 4r}{3} = 2r$.Thus,the distance of the centre of mass from $K$ is $\frac{KL + KM}{3}$.

Three identical spheres,each of mass $1 \ kg$,are placed touching each other with their centres on a straight line. Their centres are marked $K, L$,and $M$ respectively. The distance of the centre of mass of the system from $K$ is

Similar Questions

$A$ rigid body consists of a $3 \ kg$ mass and a $2 \ kg$ mass connected by a massless rod. The $3 \ kg$ mass is at $\vec{r}_1 = (2 \hat{i} + 5 \hat{j}) \ m$ and the $2 \ kg$ mass is at $\vec{r}_2 = (4 \hat{i} + 2 \hat{j}) \ m$. Find the length of the rod and the coordinates of the center of mass.

Seven identical homogeneous bricks,each of length $L$,are arranged as shown in the figure. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Calculate the $x$-coordinate of the centre of mass of this system relative to the origin $O$ as shown.

If the linear density of a rod of length $3 \ m$ varies as $\lambda = 2 + x$,then the position of the centre of mass of the rod is:

Two point masses $m$ and $M$ are separated by a distance $L$. The distance of the centre of mass of the system from $m$ is

Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat{i} + \hat{j} + \hat{k}$ and $-\hat{i} - \hat{j} - \hat{k}$ respectively would have the centre of mass at:

Vedclass Test Series

Exam Paper Generator

Online Exam Module