What is the Equilibrium Angle of an Immersed Wooden Stick?

Click For Summary
SUMMARY

The equilibrium angle of a uniform wooden stick immersed in water is determined by the relationship between the densities of the stick and the water. When the stick is in equilibrium, the tangent of the angle θ is given by the formula tanθ = d/D, where d is the density of the wooden stick and D is the density of water. This conclusion is derived from the principles of buoyancy, which dictate that the buoyant force acts at the center of the rod. Therefore, the correct answer to the problem is option (b) d/D.

PREREQUISITES
  • Understanding of buoyancy principles
  • Knowledge of density concepts
  • Familiarity with equilibrium conditions in physics
  • Basic trigonometry related to angles
NEXT STEPS
  • Study Archimedes' principle and its applications
  • Learn about the calculation of buoyant forces in fluids
  • Explore the concept of rotational equilibrium in physics
  • Investigate the effects of varying densities on buoyancy
USEFUL FOR

Students studying physics, particularly those focusing on fluid mechanics and buoyancy, as well as educators preparing lessons on equilibrium and density concepts.

nil1996
Messages
301
Reaction score
7

Homework Statement


A uniform wooden stick of density d is completely immersed in water of density D (D>d). One end of the stick is free to rotate about a hinge which is attached to the wall of the container. In equilibrium the stick the stick makes an angle θ then tanθ is-
(a)0

(b)d/D

(c)1-d/D

(d)D/d

Homework Equations



related to buoyancy

The Attempt at a Solution


First of all i am not understanding the nature of buoyant force. In this case can we consider it to act at the middle of the rod?
 
Physics news on Phys.org
Yes.
 

Similar threads

Sanity check on falling steel ball in water
  • · Replies 5 ·
Replies
5
Views
2K
Fluid Mechanics: Weight vs Pressure
  • · Replies 6 ·
Replies
6
Views
2K
Optimizing Mass for Vertical Rod Buoyancy in Unknown Fluid
  • · Replies 29 ·
Replies
29
Views
3K
What is the Tension in the String Holding a Submerged Cork?
  • · Replies 3 ·
Replies
3
Views
4K
Torque and rotational equilibrium question
  • · Replies 6 ·
Replies
6
Views
4K
Angle of Inclination of a Water Surface
  • · Replies 19 ·
Replies
19
Views
4K
Identifying all forces on this stick
  • · Replies 1 ·
Replies
1
Views
2K
Solving Mechanics Problem: Angle, Speed, Centripetal Acceleration & More
  • · Replies 12 ·
Replies
12
Views
2K
Coefficient of static friction of uniform rod
  • · Replies 2 ·
Replies
2
Views
2K
Angular acceleration, velocity, momentum of a door?
  • · Replies 88 ·
3
Replies
88
Views
24K