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Physics Guru is an online education and competitive examinations preparation portal founded by Manish Verma, an IIT Madras alumnus, providing learning resources for competitive examinations.

The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

Water in Vertical Circle

Consider a small bucket full of water tied to a string whirled around in vertical circle of radius r without water falling down. At the topmost position when the speed of the inverted bucket is v,

(A) $\frac{{{v^2}}}{r} = g$ necessarily
(B) $\frac{{{v^2}}}{r} < g$ necessarily
(C) $\frac{{{v^2}}}{r} > g$ necessarily
(D) None of the options given

Solution

Consider water as the system. Let, m be the mass of water. The weight mg acts downwards and the normal reaction N also acts downwards.

$mg + N = \frac{{m{v^2}}}{r}$

$ \Rightarrow \frac{{m{v^2}}}{r} \ge mg$

$ \Rightarrow \frac{{{v^2}}}{r} \ge g$

Hence, Option (D).