Question

A bucket full of water is tied with the help of a
2 m long string. The minimum angular velocity of
bucket at the uppermost point so that water will not
fall is
(1) 215 rad/s
(2) V5 rad/s
(4) 10 rad/s
(3) 5 rad/s

Answer 1

Answer:

Explanation:

I think the answer is 2√5 rad/s

I.e is option 1.

Answer 2

The minimum angular velocity of  bucket  is √5 rad/s

(2) is correct option.

Explanation:

Given that,

Length of string = 2 m

We need to calculate the linear velocity

Using formula of centripetal  force

$F= \dfrac{mv^2}{r}$

$mg=\dfrac{mv^2}{r}$

$v^2=rg$

Put the value into the formula

$v=\sqrt{10\times2}\ m/s$

We need to calculate the minimum angular velocity of  bucket

Using formula of angular velocity

$v = r\omega$

$\omega=\dfrac{v}{r}$

Put the value into the formula

$\omega=\dfrac{\sqrt{10\times 2}}{2}$

$\omega=\sqrt{\dfrac{10}{2}}$

$\omega=\sqrt{5}\ rad/s$

Hence, The minimum angular velocity of  bucket  is √5 rad/s

Learn more :

Topic : angular velocity

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