(C) For water not to spill out of the bucket, the bucket must complete the vertical circular motion. At the highest point, the minimum velocity requi

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(C) For water not to spill out of the bucket, the bucket must complete the vertical circular motion. At the highest point, the minimum velocity required is $v_{top} = \sqrt{gR}$. Using the principle of conservation of energy between the lowest point (bottom) and the highest point (top): $\frac{1}{2}mv_{bottom}^2 = \frac{1}{2}mv_{top}^2 + mg(2R)$ $v_{bottom}^2 = v_{top}^2 + 4gR$ $v_{bottom}^2 = gR + 4gR = 5gR$ $v_{bottom} = \sqrt{5gR}$ Given $g = 10 \,m/s^2$ and $R = 0.5 \,m$: $v_{bottom} = \sqrt{5 \times 10 \times 0.5} = \sqrt{25} = 5 \,m/s$.

Class 11 Physics Work, Energy, Power and Collision Vertical Circular Motion

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$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

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$\sqrt{5} \,m/s$
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$\sqrt{10} \,m/s$
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$5 \,m/s$
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$2\sqrt{5} \,m/s$

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$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

Similar Questions

$A$ body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration,when the string is horizontal,will be $....g$

$A$ small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the highest position is ............. $m/s$ (Take $g=10\, m/s^2$).

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