Q.

A cubic block of side a is connected with two similar vertical springs as shown. Springs were at their natural length when block is connected and then system is allowed to slowly settle in equilibrium, when bottom surface of block of density s just touches the surface of the fluid of density 2s. Now a weight is placed on the block so that it is immersed half in the fluid, find the weight

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a

aK2+a2σg

b

aK+a2σg

c

aK+a22σg

d

a2K+a2σg

answer is B.

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Detailed Solution

Initially, W – 2Kx = 0     ……(1)Finally,   W+W0−2Kx+a2−a.aa22σ⋅g=0 …….(2)From eq. (1),W0=Ka+a3σg=aK+a2σg
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A cubic block of side a is connected with two similar vertical springs as shown. Springs were at their natural length when block is connected and then system is allowed to slowly settle in equilibrium, when bottom surface of block of density s just touches the surface of the fluid of density 2s. Now a weight is placed on the block so that it is immersed half in the fluid, find the weight