A small bucket containing water is rotated in a vertical circle of radius $R$ by means of a rope. $v$ is velocity of bucket at highest point. Then water does not fall down if:

v \leq \sqrt{g R}

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v \leq \sqrt{\frac{g R}{2}}

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v \geq \sqrt{g R}

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v \geq \sqrt{\frac{g R}{2}}

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Solution

The correct option is C $v \geq \sqrt{g R}$
At highest point the centripetal acceleration should be greater than g.
$∴ \frac{v^{2}}{R} \geq g$

or, $v \geq \sqrt{R g}$

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A small bucket containing water is rotated in a vertical circle of radius R by means of a rope. v is velocity of bucket at highest point. Then water does not fall down if:

The correct option is C v≥√gRAt highest point the centripetal acceleration should be greater than g.∴v2R≥gor, v≥√Rg

A small bucket containing water is rotated in a vertical circle of radius $R$ by means of a rope. $v$ is velocity of bucket at highest point. Then water does not fall down if:

The correct option is C $v \geq \sqrt{g R}$
At highest point the centripetal acceleration should be greater than g.
$∴ \frac{v^{2}}{R} \geq g$

or, $v \geq \sqrt{R g}$