Q129 / 160 · AP EAMCET 2007 · Physics

A bucket filled with water is tied to a rope of length $0.5 \mathrm{~m}$ and is rotated in a circular path in vertical plane. The least velocity it should have at the lowest point of circle so that water does not spill is, $\left(g=10 \mathrm{~ms}^{-2}\right)$

A
$\sqrt{5} \mathrm{~m} / \mathrm{s}$
B
$\sqrt{10} \mathrm{~m} / \mathrm{s}$
Correct answer
C
$5 \mathrm{~m} / \mathrm{s}$
D
$2 \sqrt{5} \mathrm{~m} / \mathrm{s}$

Solution

For water not to spill out of the bucket, $\begin{aligned} v_{\min } & =\sqrt{5 g R} \\ & =\sqrt{5 \times 10 \times 0.5} \\ & =5 \mathrm{~m} / \mathrm{s}\end{aligned}$

Hence, the correct answer is option: 'C'.

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