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Question

A cubical block of wood of edge 3cm floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. Find the maximum weight that can be put on the block without wetting the new weight. Density of wood =800kg/m3 and spring constant of the spring=50N/m.(Take g=10m/s2)
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Solution

Fraction of volume immersed before putting the new weight=ρblockρwater
=8001000
=0.8
i.e., 20% of 3 cm or 0.6 cm is above water. Let W is the new weight, then spring will be compressed by 0.6 cm.
W+weight of block=Upthrust on whole volume of block+spring force
or
W=(3×102)3×1000×10+50×(0.6×102)(3×102)3×800×10
W=0.354 N

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