
A cylindrical vessel partially filled with water is rotated about its vertical central axis, it's surface will
A. Rise equally
B. Rise from sides
C. Rise from the middle
D. Lowered equally
Answer
164.1k+ views
Hint:When a body is rotated about an axis then there is centripetal acceleration acting towards the center of the circular path described by the rotatory motion. The fluid pressure at the same horizontal level is equal.
Formula used:
\[P = \rho gh + \rho al\]
Where P is the fluid pressure at depth h from the surface of the water in an accelerated container with acceleration a and the distance from the center is $l$.
\[{a_c} = {\omega ^2}r\]
Here \[\omega \] is the angular speed with which the cylinder is rotated.
Complete step by step solution:
When a cylindrical vessel which is partially filled with water is rotated then the total pressure at the bottom of the container is due to fluid pressure, atmospheric pressure and the centripetal force acting per unit area.

Image: A rotating cylinder with water
Taking two points on the same horizontal level. When the cylinder is rotated about its own axis then the centripetal force will act towards the center of the cylinder. The centripetal acceleration is given as,
\[{a_c} = {\omega ^2}r\]
Then the pressure at point A will be,
\[{P_A} = {P_0}\]
And the pressure at point B will be,
\[{P_B} = {P_0} - {\omega ^2}r\]
As both the points are on the same horizontal level, so the pressure at both the points at equilibrium must be the same. To balance the pressure, the water will rise above the horizontal level so that there is extra pressure due to fluid. And hence, the water surface will take a concave upward shape, i.e. the water will rise from the sides.
Therefore, the correct option is B.
Note: When the cylinder is at rest then the surface of the water will be horizontal so that every point on the same horizontal level has the same pressure. Moreover, the measurement of the force per unit area on an item on the surface of a closed container or in the fluid is known as fluid pressure. This pressure is brought on by acceleration, gravity, or external forces in closed containers.
Formula used:
\[P = \rho gh + \rho al\]
Where P is the fluid pressure at depth h from the surface of the water in an accelerated container with acceleration a and the distance from the center is $l$.
\[{a_c} = {\omega ^2}r\]
Here \[\omega \] is the angular speed with which the cylinder is rotated.
Complete step by step solution:
When a cylindrical vessel which is partially filled with water is rotated then the total pressure at the bottom of the container is due to fluid pressure, atmospheric pressure and the centripetal force acting per unit area.

Image: A rotating cylinder with water
Taking two points on the same horizontal level. When the cylinder is rotated about its own axis then the centripetal force will act towards the center of the cylinder. The centripetal acceleration is given as,
\[{a_c} = {\omega ^2}r\]
Then the pressure at point A will be,
\[{P_A} = {P_0}\]
And the pressure at point B will be,
\[{P_B} = {P_0} - {\omega ^2}r\]
As both the points are on the same horizontal level, so the pressure at both the points at equilibrium must be the same. To balance the pressure, the water will rise above the horizontal level so that there is extra pressure due to fluid. And hence, the water surface will take a concave upward shape, i.e. the water will rise from the sides.
Therefore, the correct option is B.
Note: When the cylinder is at rest then the surface of the water will be horizontal so that every point on the same horizontal level has the same pressure. Moreover, the measurement of the force per unit area on an item on the surface of a closed container or in the fluid is known as fluid pressure. This pressure is brought on by acceleration, gravity, or external forces in closed containers.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
