A circular plate of radius r is removed from | vedclass

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

Question

(C) Let the mass per unit area of the plate be $\sigma$.Mass of the original plate $M = \sigma \pi (4r)^2 = 16 \sigma \pi r^2$.Mass of the removed cir

Vedclass · Accepted Answer

$\frac{2 r}{15}$

Vedclass · Answer

(C) Let the mass per unit area of the plate be $\sigma$.Mass of the original plate $M = \sigma \pi (4r)^2 = 16 \sigma \pi r^2$.Mass of the removed circular part $m = \sigma \pi r^2$.The mass of the remaining portion is $M' = M - m = 16 \sigma \pi r^2 - \sigma \pi r^2 = 15 \sigma \pi r^2$.Let the centre of the original plate be at the origin $(0, 0)$.The centre of the removed part is at $(2r, 0)$.Using the principle of centre of mass for a cavity: $M X_{CM} = M' X_{R} + m X_{C}$,where $X_{CM}$ is the centre of mass of the original plate (which is $0$),$X_{R}$ is the centre of mass of the remaining portion,and $X_{C}$ is the centre of mass of the removed part.$0 = (15 \sigma \pi r^2) X_{R} + (\sigma \pi r^2)(2r)$.$15 X_{R} = -2r$.The magnitude of the distance is $|X_{R}| = \frac{2r}{15}$.

Similar Questions

$A$ semicircular portion of radius $r$ is cut from a uniform rectangular plate as shown in the figure. The distance of the centre of mass $C$ of the remaining plate from point $O$ is:

In the figure shown,find the distance of the centre of mass of a system of a uniform circular plate of radius $3R$ from $O$,in which a hole of radius $R$ is cut whose centre is at a distance of $2R$ from the centre of the large circular plate.

$A$ uniform square plate is shown in the figure. Four identical small squares are removed from its corners. Where will the $C.M.$ (Center of Mass) be located after removing all four squares? Give the answer in terms of quadrants and axes.

$A$ sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass is at the maximum distance from the original centre. What is this distance?

$A$ solid cone is placed on a horizontal surface has height $h$,radius $R$ and apex angle $\theta$ as shown. If the gravitational potential energy of the cone does not change as the position of the cone is changed from figure $(A)$ to figure $(B)$,then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module