In the figure,one-fourth part of a uniform di | vedclass

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

Question

(A) Let the disc lie in the $xy$-plane with its centre at the origin $O(0,0)$. The disc occupies the first quadrant.Due to symmetry about the line $y=

Vedclass · Accepted Answer

$\sqrt{2} \frac{4R}{3\pi}$

Vedclass · Answer

(A) Let the disc lie in the $xy$-plane with its centre at the origin $O(0,0)$. The disc occupies the first quadrant.Due to symmetry about the line $y=x$,the centre of mass $(X_{cm}, Y_{cm})$ must lie on this line,so $X_{cm} = Y_{cm}$.For a semi-circular disc of radius $R$,the centre of mass is at a distance $\frac{4R}{3\pi}$ from the diameter along the axis of symmetry.For a quarter disc,the centre of mass coordinates are $X_{cm} = \frac{4R}{3\pi}$ and $Y_{cm} = \frac{4R}{3\pi}$.The distance of the centre of mass from the origin $O$ is given by $d = \sqrt{X_{cm}^2 + Y_{cm}^2}$.$d = \sqrt{\left(\frac{4R}{3\pi}\right)^2 + \left(\frac{4R}{3\pi}\right)^2} = \sqrt{2 \left(\frac{4R}{3\pi}\right)^2} = \sqrt{2} \frac{4R}{3\pi}$.

In the figure,one-fourth part of a uniform disc of radius $R$ is shown. The distance of the centre of mass of this object from the centre $O$ is:

Similar Questions

If the density of the material of a circular plate and a square plate as shown is the same,the center of mass of the composite system will be:

Four particles of masses $m, 2m, 3m, 4m$ are placed at the corners of a square of side $a$ as shown in the figure. Find the coordinates of the center of mass.

The integral $\int \vec{r} dm = 0$ for a homogeneous body is defined for which point?

Two bodies of mass $1 \ kg$ and $3 \ kg$ have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$,respectively. The centre of mass of this system has a position vector:

Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat{i} + \hat{j} + \hat{k}$ and $-\hat{i} - \hat{j} - \hat{k}$ respectively would have the centre of mass at:

Vedclass Test Series

Exam Paper Generator

Online Exam Module