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Q.

A cubical block of wood of side a and density ρ floats in water of density 2ρ. The lower surface of the cube just touches the free end of a massless spring of force constantk fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

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a

aa2ρg+k

b

a(aρg+2k)

c

aaρg2+2k

d

aa2ρg+k2

answer is D.

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Detailed Solution

Since density of block is 1/2(density of water), 50% of its volume is immersed in water.In the second case, half of the volume of the block is further immersed in water.Therefore, W=Extra upthrust + Spring force=Buoyant force + Spring force =Vi×ρl×g+kx =a×a×a2×2ρ×g+ka2 =aa2ρg+k2
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