The maximum time period of a bucket full of water whirled in a vertical circle of radius 10m so that the water may not fall is (g = 10 ms^–2)

R = 10m

At highest point water should accelerate at a rate of g if it is not falling.

$\frac{{\mathrm{V}}^2}{\mathrm{R}}=\mathrm{g}$

$\Rightarrow \mathrm{V}=\sqrt{\mathrm{Rg}}=\sqrt{10\times 10}=10\mathrm{m}/\mathrm{s}$

The minimum speed at which a bucket should be spun is 10 m/s.
Let's assume that speed is constant.

$\mathrm{T}=\frac{2\mathrm{\pi r}}{\mathrm{V}}=\frac{2\mathrm{\pi }\times 10}{10}=2\mathrm{\pi } \mathrm{s}$

Hence the correct answer is$2\mathrm{\pi }$s