wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Two identical cylindrical vessels, each of base area A, have their bases at the same horizontal level. They contain a liquid of density ρ. In one vessel, the height of the liquid is h1 and in the other h2>h1. When the two vessels are connected, the work done by gravity in equalizing the levels is


A

2ρAg(h2h1)2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

ρAg(h2h1)2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

12ρAg(h2h1)2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

14ρAg(h2h1)2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

14ρAg(h2h1)2


Let the liquid from height h2 come down through a distance x. In the other vessel, liquid will rise by the same amount x.
Hence, h2x=h1+xx=h2h12
Thus, effectively a slab of liquid 12(h2h1) in thickness falls a vertical distance equal to its thickness under the action of gravity.
Work done by the gravity, W=mg×12(h2h1)
where mass of the slab m is given by
m=ρ×V=ρ×12(h2h1)×A
W=12ρ(h2h1)×A×g×12(h2h1)=14ρAg(h2h1)2
Hence, the correct choice is (d).


flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Work done by the force of gravity
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon