A uniform square plate abcd has a mass of 1 , | vedclass

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

Question

(C) Let the side length of the square plate be $L$. The center of the square $O$ is at the origin $(0,0)$.The coordinates of the corners are: $a(-L/2,

Vedclass · Accepted Answer

$OY$

Vedclass · Answer

(C) Let the side length of the square plate be $L$. The center of the square $O$ is at the origin $(0,0)$.The coordinates of the corners are: $a(-L/2, L/2)$,$b(L/2, L/2)$,$c(L/2, -L/2)$,and $d(-L/2, -L/2)$.The mass of the plate $M = 1 \, kg = 1000 \, g$ is concentrated at the center $O(0,0)$.Two point masses $m = 20 \, g$ are placed at $b(L/2, L/2)$ and $c(L/2, -L/2)$.The new $x$-coordinate of the center of mass is $X_{cm} = \frac{M(0) + m(L/2) + m(L/2)}{M + 2m} = \frac{mL}{M + 2m}$.The new $y$-coordinate of the center of mass is $Y_{cm} = \frac{M(0) + m(L/2) + m(-L/2)}{M + 2m} = 0$.Since $Y_{cm} = 0$ and $X_{cm} > 0$,the center of mass shifts along the positive $x$-axis,which corresponds to the line $OY$.

$A$ uniform square plate $abcd$ has a mass of $1 \, kg$. If two point masses,each of $20 \, g$,are placed at the corners $b$ and $c$ as shown,then the centre of mass shifts on the line

Similar Questions

When does a body (system) have different centre of gravity and centre of mass?

$A$ square plate and a circular disc of uniform density are arranged as shown in the figure. The center of mass of this combined system will be .........

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:

Three identical spheres,each of mass $1 \ kg$,are arranged as shown in the figure. If their centers of mass are at $P$,$Q$,and $R$ respectively,what is the distance of the center of mass of this system from point $P$?

Two point masses of $1.5 \ g$ and $2.5 \ g$ are placed at a distance of $16 \ cm$ from each other. If the center of mass is at a distance $x$ from the $1.5 \ g$ mass,then $x = \dots \ cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module