Question

an open cylindrical vessel having a base radius of 500mm and 2.5m tall is 3/5 full of water. the vessel is rotated about its vertical axis at a constant angular speed

Answer 1

it was very easy

do only the formula and get your answer

Answer 2

The value of constant angular speed of the vessel is 14.14 rad/sec.

Given:-

Radius of the cylindrical vessel = 500mm

Height of the cylindrical vessel = 2.5m

Height upto which water is filled = 3/5

To Find:-

The value of constant angular speed of the vessel.

Solution:-

We can easily calculate the value of constant angular speed of the vessel by using the following procedure.

As

Radius of the vessel (r) = 500mm = 0.5m

Height of the cylindrical vessel (H) = 2.5m

Height upto which water is filled = 3/5

Actual height upto which water is filled = 3/5×2.5

h = 1.5m

Now, According to the formula,

$h = \frac{ {w}^{2} \times {r}^{2} }{2g}$

${w}^{2} = \frac{2gh}{ {r}^{2} }$

on putting the values,

${w}^{2} = \frac{2 \times 10 \times 2.5}{ {0.5}^{2} }$

${w}^{2} = \frac{2 \times 25}{0.5 \times 0.5}$

${w}^{2} = \frac{2 \times 25}{0.25}$

${w}^{2} = \frac{2 \times 25 \times 100}{25}$

${w}^{2} = 2 \times 100$

${w}^{2} = 200$

$w = \sqrt{200}$

$w = 14.14$

Hence, The value of constant angular speed of the vessel is 14.14 rad/sec.

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