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Q.

A cubic block of side a is connected with two similar vertical springs as shown. Initially bottom surface of block of density σ touches the surface of the fluid of density 2σ while floating. A weight of negligble volume is placed on the block so that it is immersed half in the fluid. Find the weight.

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a

αK2+α2σ g

b

α K+α2σ g

c

αK+α22 σ g

d

α2K+α2σ g

answer is B.

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Detailed Solution

Initially, W-2 Kx=0 .....(1)

Finally, W '-2K x+α2-α.α.α22σ.g=0=...(2)

W '=W+ W0     W+W0-2Kx-Kα-α3σ,g=0

[From eqn. (2)] From eqn (1)

W0=Ka+a3σg=aK+a3σg

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