IIT JEE , AIEEE Forum - Physics , Mechanics

umang

Given two vessels having same base area and water filled to the same height . Now , the force exerted by water on base of both vessels is same , then why do vessels filled with water give different readings on weighing scales .

I would appreciate if the answer is well explained !!!!!

raman_1290

are the vessels identical and of same material?

avdesh100

it ways differently due to the shape of the vessels

umang

I am sorry I forgot to add one information !

The volume of water in vessel A is more than that in vessel B . So , u can imagine the shape . Also , they are of same materials .

Pls reply with solution !!!!!

raman_1290

yaar, if A has more volume of water then obviosly it will weigh more than B because, mass = density X volume, which is greater in case of A

truly

consider 2 vesseles one(A) which is cylindrical with base radius b and water filled to a hight h, and other(B) a frustum of cone with base radius b at bottom and radius 2b at a hight h to which the water is filled. Assume tht weights of vessels is negligible compared whn filled with water.
density of water = p

Case 1: force on base.....

pressure depends on hight so in both cases pressure at the base = pgh

on A ..... pgh x area of base (pib^2) = pgh pi b^2

on B ..... pgh x area of base (pib^2) = pgh pi b^2

Hence same force on base.....

Case 2 : Reading on weighing scale.

mass of water in A = Volume of A x p
                            = (pi b^2 x h) x p
weight of A = mass of water in A x g = pi b^2 hpg ............1

mass of water in B = Volume of B x p

I am writing down directly the volume of vessel B as it is easy to find out the volume.

                            =( (7/3) x pi b^2 x h) x p
weight of B = mass of water in B x g = (7/3) pi b^2 hpg ............2

YOU can see tht weight of A & B are different and thus the scale readings.

Ne queries

rao_prabhat

The forces exerted by the fluid in the two vessels on their bases are equal because the pressure depends on the height of the column regardless of the shape and column of the vessel. This is because of the way by which the expression P=rho*g*h. But the weight of the fluid is given by rho*g*V where the V is the volume of the fluid.
---Hope This Helps
--Prabhat rao
Give your rate

rao_prabhat

The liquid exerts pressure and hence force, not only on the base but also on the walls on the container. This force is perpendicular to the wall of the container. Now consider two types of vessel one conical shaped one (P) and the other a container just straight(R). Now along the walls of the container P there is a non-zero component pointing vertically downwards (force caused due to pressure). But the container R has no downward component. There fore when there are placed on the weighing scale container P records greater weight than that of container B
This is conceptual approach to the problem. It made really think hard. Thanks
--- Hope this helps
----Expecting for a higher rate
---Prabhat rao

kghedriu

Weighing machines read amount of normal force...which is equal to weight here, bcos of no additional force....and since different volumes are filled, different weights are noted and so we have different readings..

rao_prabhat

sorry I said in my previous reply to consider a conical shaped vessed. It is not a conical shaped vessel but consider it to be bucket shaped container

Sorry

umang

Thank you all for answering !!!!!!!!

pinnaka

I think prabhat is correct

rao_prabhat

please say whether I am correct or not by a giving a rate

umar360

i think it is due to irregular surface (curved surface)of the vessel / body. the forces exerted by the liquid on the wall r not parallel to the base.

may it be the answer, if not please mail me dear ok. bye

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