The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position x/3a/π, x/3a/π where x is _____________. (Round off to the Nearest Integer). [a is an area as shown in the figure] Numerical answer type. Work it out, then open the answer.

Answer: 4. In the figure a is the radius of the disc. For a uniform quarter disc of radius a, xcm = ycm = (4a)/(3π). Comparing with x/3a/π: x = 4

The disc of mass M with uniform surface mass density σ is shown in… | JEE Main 2021 (17 Mar, Shift 2)

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Continuous Bodies: Standard Results & Variable Density

The disc of mass M with uniform surface mass density $\sigma$ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position $\frac{x}{3}\frac{a}{\pi}, \frac{x}{3}\frac{a}{\pi}$ where x is _____________. (Round off to the Nearest Integer).

[a is an area as shown in the figure]

Numerical answer type. Work it out, then open the answer.

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Answer: 4

In the figure $a$ is the radius of the disc.
For a uniform quarter disc of radius $a$ , $x_{cm} = y_{cm} = \frac{4a}{3\pi}$ .
Comparing with $\frac{x}{3}\frac{a}{\pi}$ : $x = 4$

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