A circular portion of radius R_2 has been rem | vedclass

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

Question

(A) Let the original disc have radius $R_1$ and mass $M_1 = \sigma \pi R_1^2$,where $\sigma$ is the surface mass density. Its center of mass is at the

Vedclass · Accepted Answer

$-\frac{R_2^2}{R_1+R_2}$

Vedclass · Answer

(A) Let the original disc have radius $R_1$ and mass $M_1 = \sigma \pi R_1^2$,where $\sigma$ is the surface mass density. Its center of mass is at the origin $(0,0)$.Let the removed circular portion have radius $R_2$ and mass $M_2 = \sigma \pi R_2^2$. Its center is at $(R_1 - R_2, 0)$ as shown in the figure.The center of mass of the remaining portion is given by:$x_{CM} = \frac{M_1 x_1 - M_2 x_2}{M_1 - M_2}$Substituting the values:$x_{CM} = \frac{(\sigma \pi R_1^2)(0) - (\sigma \pi R_2^2)(R_1 - R_2)}{\sigma \pi R_1^2 - \sigma \pi R_2^2}$$x_{CM} = \frac{-R_2^2(R_1 - R_2)}{R_1^2 - R_2^2}$$x_{CM} = \frac{-R_2^2(R_1 - R_2)}{(R_1 - R_2)(R_1 + R_2)}$$x_{CM} = -\frac{R_2^2}{R_1 + R_2}$

$A$ circular portion of radius $R_2$ has been removed from one edge of a circular disc of radius $R_1$. The correct expression for the centre of mass for the remaining portion of the disc is

Similar Questions

The position of the centre of mass of the uniform plate as shown in the figure is

$A$ circular plate $A$ of radius $1.5 r$ is removed from one edge of a uniform circular plate $B$ of radius $2 r$. The distance of the centre of mass of the remaining portion from the centre of the plate $B$ is

$A$ circular plate of uniform thickness has a diameter of $56 \ cm$. $A$ circular part of diameter $42 \ cm$ is removed from one edge. What is the position of the centre of mass of the remaining part in $cm$?

$A$ uniform square plate of side $a$ has a circular hole of diameter $a$ cut out from it as shown in the figure. The centre of the hole is at the centre of the square. The centre of mass of the remaining part is:

For the given uniform square lamina $ABCD$ whose centre is $O$,pick the incorrect statement.

Vedclass Test Series

Exam Paper Generator

Online Exam Module