The masses and positions (in rectangular coor | vedclass

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

Question

(D) The position vector of the center of mass $(COM)$ of a system of particles is given by:$r_{COM} = \frac{m_1 r_1 + m_2 r_2 + m_3 r_3 + m_4 r_4}{m_1

Vedclass · Accepted Answer

$-0.4 a \hat{j}$

Vedclass · Answer

(D) The position vector of the center of mass $(COM)$ of a system of particles is given by:$r_{COM} = \frac{m_1 r_1 + m_2 r_2 + m_3 r_3 + m_4 r_4}{m_1 + m_2 + m_3 + m_4}$Given masses and positions:$m_1 = 1 \ kg, r_1 = (a \hat{i} + a \hat{j})$$m_2 = 2 \ kg, r_2 = (-a \hat{i} + a \hat{j})$$m_3 = 3 \ kg, r_3 = (-a \hat{i} - a \hat{j})$$m_4 = 4 \ kg, r_4 = (a \hat{i} - a \hat{j})$Total mass $M = 1 + 2 + 3 + 4 = 10 \ kg$$r_{COM} = \frac{1(a \hat{i} + a \hat{j}) + 2(-a \hat{i} + a \hat{j}) + 3(-a \hat{i} - a \hat{j}) + 4(a \hat{i} - a \hat{j})}{10}$$r_{COM} = \frac{(a - 2a - 3a + 4a) \hat{i} + (a + 2a - 3a - 4a) \hat{j}}{10}$$r_{COM} = \frac{0 \hat{i} - 4a \hat{j}}{10} = -0.4 a \hat{j}$

The masses and positions (in rectangular coordinates) of four particles are as follows: $1 \ kg$ at $(a, a)$,$2 \ kg$ at $(-a, a)$,$3 \ kg$ at $(-a, -a)$,and $4 \ kg$ at $(a, -a)$. The position vector of the centre of mass of the system of four particles is:

Similar Questions

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:

Infinite numbers of blocks are placed on a table edge as shown in the diagram. What is the minimum value of $L$ so that the blocks are just going to topple over the table?

The centre of mass of a triangle shown in the figure has coordinates

$A$ straight rod of length $L$ has one of its ends at the origin and the other at $x = L$. If the mass per unit length of the rod is given by $\lambda = Ax$ (where $A$ is a constant),then where is its center of mass from the origin?

Vedclass Test Series

Exam Paper Generator

Online Exam Module