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

$A$ uniform thin rod of length $L$ and mass $M$ is placed along the $x$-axis with one end at the origin. Find the position of the centre of mass of the rod.

$A$ slender uniform rod of length $L$ is balanced vertically at a point $P$ on a horizontal surface having some friction. If the top of the rod is displaced slightly to the right,the position of its centre of mass at the time when the rod becomes horizontal is:

The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$,where $k$ is a constant and $x$ is the distance from one end. The position of the centre of mass of the rod is:

Which of the following statements regarding the centre of mass is $NOT$ true?

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 $80 \, cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module