### JEE Main 12 Jan 2019 Evening Question 5

##### Question: A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be [JEE Main Online Paper Held On 12-Jan-2019 Evening]

#### Options:

A) 0.4

B) 2.0

C) 0.1

D) 1.2

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

- The linear speed of the liquid at the sides is $ r\omega $ .

So, the difference in height is given as follows: $ 2gh=w^{2}r^{2} $

$ \Rightarrow $ $ h=\frac{{{(2\times 2\pi )}^{2}}{{(5\times {10^{-2}})}^{2}}}{2\times 10}\approx 0.02m $