Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density ρ (rho). The height of the liquid in one vessel is h 1 and in other is h ­2 . The area of either base is A. What is the work done by gravity in equalizing the levels when the tow vessels are connected?

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density ρ (rho). The height of the liquid in one vessel is h1 and in other is h­2. The area of either base is A. What is the work done by gravity in equalizing the levels when the tow vessels are connected?     

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Hello Student,
Please find the answer to your question
P.E. of liquid in cylinder 1
U1 = (m) g h1 / 2 = ( ρ x A x h1 ) g h1 / 2 = ρAgh21 / 2
Note :
[The total mass can be supposed to be concentrated at the center of the filled part which will be at height h­1 / 2]
Similarly P.E. of liquid in cylinder 2 U2 = ρAgh22 / 2
∴ Total P.E. initially U = U1­ + U2 (h21 + h2­2)
After the equalising of levels.
P.E. of liquid in cylinder 1 U1 = mg h / 2 = ρAg / 2 h2
P.E. of liquid in cylinder 2 U2’ = mg h / 2 = ρAg / 2 h2
∴ Total P.E. finally U’ = U1’ + U2’ = ρAgh2
The change in P.E.
∆U = U – U’ = ρAg [h21 / 2 + h22 / 2 – h2]
Total volume remains the same.
Ah1 + Ah2 = Ah + Ah
⇒ h = h1 + h2 / 2
Therefore,
∆U = ρAg [h21 / 2 + h22 / 2 – (h1 + h2 / 2)2]
= ρAg / 4 (h1 – h2)2
This change in P.E. is the work done by gravity
Thanks
Kevin Nash
askIITians Faculty
ankit singh
askIITians Faculty 614 Points
8 months ago
wo identical cylindrical vessels with their bases at the same levelTwo identical cylindrical vessel with their bases at the same level each contain a liquid of density ρ. The height of the liquid in one vessel is h1 and in the other is h2 the area of either base is A

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free