As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation
As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation
- [JEE MAIN 2020]
- A
$\left(\mathrm{R}^{2}-\mathrm{R}+1\right)(2-\mathrm{R})=1$
- B
$\left(\mathrm{R}^{2}+\mathrm{R}-1\right)(2-\mathrm{R})=1$
- C
$\left(\mathrm{R}^{2}+\mathrm{R}+1\right)(2-\mathrm{R})=1$
- D
$\left(\mathrm{R}^{2}-\mathrm{R}-1\right)(2-\mathrm{R})=1$
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