A square plate of side 12 cm is shown in the | vedclass

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

Question

(A) Let the mass of the original square plate be $M$. Let the mass of the small square piece cut out be $m$. The mass of the remaining part is $(M - m

Vedclass · Accepted Answer

$\left( - \frac{5m}{M - m}, - \frac{5m}{M - m} \right) \ cm$

Vedclass · Answer

(A) Let the mass of the original square plate be $M$. Let the mass of the small square piece cut out be $m$. The mass of the remaining part is $(M - m)$.The center of mass of the original plate of mass $M$ is at $(0, 0)$.The center of mass of the cut-out square piece of mass $m$ is at $(5, 5) \ cm$ (since the side is $12 \ cm$,the corner is at $(6, 6)$,and the center of a $2 \ cm$ square at that corner is at $(6-1, 6-1) = (5, 5)$).Let the center of mass of the remaining part of mass $(M - m)$ be $(x, y)$.Using the principle of center of mass: $M(0, 0) = m(5, 5) + (M - m)(x, y)$.This gives $m(5, 5) + (M - m)(x, y) = (0, 0)$.Equating the $x$ and $y$ components:$5m + (M - m)x = 0 \implies x = - \frac{5m}{M - m}$.$5m + (M - m)y = 0 \implies y = - \frac{5m}{M - m}$.Thus,the center of mass is $\left( - \frac{5m}{M - m}, - \frac{5m}{M - m} \right) \ cm$.

$A$ square plate of side $12 \ cm$ is shown in the figure. If a square of side $2 \ cm$ is cut from one of its corners,where will the center of mass of the remaining part be with respect to the center of the original square? The plate has uniform thickness and density.

Similar Questions

The sector of a circular plate shown in the figure has its center of mass at $y_{CM} =$

From a circular disc of radius $R$,a square is cut out with a radius as its diagonal. The center of mass of the remaining part is at a distance (from the centre) of:

In the figure shown,a hole of radius $2 \, cm$ is made in a semicircular disc of radius $6 \, cm$ at a distance $8 \, cm$ from the centre $C$ of the disc. The distance of the centre of mass of this system from point $C$ is ......... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module