Four masses are arranged along a circle of ra | vedclass

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

Question

(A) The coordinates of the masses arranged on the circle of radius $R = 1 \ m$ are:$M$ at $(1, 0)$$2M$ at $(0, 1)$$3M$ at $(-1, 0)$$4M$ at $(0, -1)$Th

Vedclass · Accepted Answer

$-\frac{1}{5} \hat{i} - \frac{1}{5} \hat{j}$

Vedclass · Answer

(A) The coordinates of the masses arranged on the circle of radius $R = 1 \ m$ are:$M$ at $(1, 0)$$2M$ at $(0, 1)$$3M$ at $(-1, 0)$$4M$ at $(0, -1)$The $x$-coordinate of the center of mass $(X_{cm})$ is given by:$X_{cm} = \frac{M(1) + 2M(0) + 3M(-1) + 4M(0)}{M + 2M + 3M + 4M} = \frac{M - 3M}{10M} = \frac{-2M}{10M} = -\frac{1}{5} \ m$The $y$-coordinate of the center of mass $(Y_{cm})$ is given by:$Y_{cm} = \frac{M(0) + 2M(1) + 3M(0) + 4M(-1)}{M + 2M + 3M + 4M} = \frac{2M - 4M}{10M} = \frac{-2M}{10M} = -\frac{1}{5} \ m$Thus,the position vector of the center of mass is $-\frac{1}{5} \hat{i} - \frac{1}{5} \hat{j}$.

Four masses are arranged along a circle of radius $1 \ m$ as shown in the figure. The center of mass of this system of masses is at

Similar Questions

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

The centre of mass of three particles of masses $1 \ kg, 2 \ kg$ and $3 \ kg$ is at $(2, 2, 2)$. The position of the fourth mass of $4 \ kg$ to be placed in the system so that the new centre of mass is at $(0, 0, 0)$ is:

Consider 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?

Obtain the position of the centre of mass of a thin rod of uniform density.

In the figure,one-fourth part of a uniform disc of radius $R$ is shown. The distance of the centre of mass of this object from the centre $O$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module