Question

Consider a hollow sphere with centre at origin. find the distance of centre of mass of 1/4 th of the hollow sphere from origin

• A. R/8
• B. R/4
• C. R*sqrt(2)/8
• D. R/2

Answer 1

Answer: (C)

The distance of the center of mass of 1/4th of the hollow sphere from origin is $\frac{R\sqrt{2}}{8}$.

Answer 2

• Explanation of the solution: The center of mass of a quarter hollow sphere (defined by $0 \le \phi \le \pi/2$, $0 \le \theta \le \pi$) is calculated by integrating the position vector weighted by the mass element over the specified region. For a uniform hollow sphere of radius $R$, the coordinates of the center of mass of the quarter sphere are $(R/8, R/8, 0)$. The distance from the origin is then found using the distance formula: $d = \sqrt{X_{com}^2 + Y_{com}^2 + Z_{com}^2} = \sqrt{\left(\frac{R}{8}\right)^2 + \left(\frac{R}{8}\right)^2 + 0^2} = \sqrt{\frac{R^2}{64} + \frac{R^2}{64}} = \sqrt{\frac{2R^2}{64}} = \frac{R\sqrt{2}}{8}$.