Three rods of the same mass are placed as sho | vedclass

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

Question

(C) Let the three rods be $R_1$,$R_2$,and $R_3$ with mass $m$ each.$1$. Rod $R_1$ lies on the $x$-axis from $(0,0)$ to $(2a,0)$. Its centre of mass is

Vedclass · Accepted Answer

$\left(\frac{2a}{3}, \frac{a}{3}\right)$

Vedclass · Answer

(C) Let the three rods be $R_1$,$R_2$,and $R_3$ with mass $m$ each.$1$. Rod $R_1$ lies on the $x$-axis from $(0,0)$ to $(2a,0)$. Its centre of mass is at $(x_1, y_1) = (a, 0)$.$2$. Rod $R_2$ lies on the $y$-axis from $(0,0)$ to $(0,a)$. Its centre of mass is at $(x_2, y_2) = (0, a/2)$.$3$. Rod $R_3$ connects $(2a,0)$ and $(0,a)$. Its centre of mass is at $(x_3, y_3) = (a, a/2)$.The coordinates of the centre of mass $(X_{cm}, Y_{cm})$ are given by:$X_{cm} = \frac{m(x_1 + x_2 + x_3)}{3m} = \frac{a + 0 + a}{3} = \frac{2a}{3}$$Y_{cm} = \frac{m(y_1 + y_2 + y_3)}{3m} = \frac{0 + a/2 + a/2}{3} = \frac{a}{3}$Thus,the centre of mass is at $\left(\frac{2a}{3}, \frac{a}{3}\right)$.

Three rods of the same mass are placed as shown in the figure. The coordinates of the centre of mass of the system are:

Similar Questions

The centre of mass of two thin uniform rods of the same length $L$ but made of different materials and kept as shown in the figure can be,if the meeting point is the origin of coordinates:

Particles of masses $8 \, kg, 2 \, kg, 4 \, kg$,and $2 \, kg$ are placed at the vertices $A, B, C$,and $D$ of a square respectively. The distance of the center of mass of the system from vertex $A$ is $....... \, cm$. The length of the diagonal of the square is $80 \, cm$.

Four bodies of masses $2\,kg, 3\,kg, 5\,kg$ and $8\,kg$ are placed at the four corners of a square of side $2\,m$ as shown in the figure. The position of the centre of mass $(CM)$ is:

What is the torque acting on the center of mass of an object due to the gravitational force?

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module