A metal ball, suspended from a thin thread, is lowered into a beaker containing a liquid (Fig.). The ball is then raised through a height h. Its potential energy will clearly now have increased by mgh, where m is the mass of the ball. On the other hand, a volume of liquid equal to the volume of the ball v, will move downwards from position 2 to position 1, i.e. its potential energy will decrease by v ρ gh, where ρ is the density of the liquid. The potential energy of the whole system (that is, ball-liquid) has been altered. How can Archimedes's law be deduced from these considerations about energy?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. When the metal ball is moved from position 1 to position 2 in the liquid, work must be done equal to the change in potential energy of the system, i.e. mgh–v ρ gh or (m–v ρ ) gh. Since the distance between 1 and 2 is h, the force which must be applied to raise the ball is (m–v ρ ) g.This force is less than the weight of the ball by an amount v ρ g, i.e. by the weight of a volume of liquid equal to the volume of the body. Thus we have reached the usual formulation of Archimedes' principle
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems