Fluid Problem: Force on a Metal Cube Immersed in Water

[koolraj]

Homework Statement

metal cube is placed in an empty vessel. When water is
filled in the vessel so that the cube is completely immersed in the
water, the force on the bottom of the vessel in contact with the
cube:
(a) Will decrease
(b) Will increase
(c) Will remain same
(d) Will become zero

i tried the ans i think it's (a) will decrease.but book say's (c)it remains constant

Homework Equations

The Attempt at a Solution

Consider the two cases case1) when vessel is empty
Case2) when vessel is filled with water
Let w=weight of the metal cube (in air)
N=normal reaction exerted by cube on the vessel in absence of water
R= normal reaction exerted by cube on the vessel in presence of water
B= Buoyancy force (=weight of fluid displaced by the block)
Then by drawing the free body diagram of metal cube in each case as shown in fig. above we have
Case 1)w=N
Case 2)w=R+B
i.e. R=w-B. Thus the reaction on cube(by the vessel) in presence of water decreases due to the Buoyant force. Hence, the force on the bottom of the vessel in contact with the cube decreases

 

[redargon]

I agree with your answer and not that of the book. Maybe we're missing something?