A cubical block of wood of edge 3 cm 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 it. Density of wood =`800 kgm^-3` and spring constant of the spring `=50Nm^-1 Take g=10ms^-2`.
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Answer

C, D

Explanation

Fraction of volume immersed before putting the new weigh `=(rho_(block))/(rho_(water))=(800)/(1000)=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=(3xx10^(-2))^(3)xx1000xx10+50xx`
`(0.6xx10^(-2))=(3xx10^(-2))^(3)xx800xx10`
`:. w=0.354 N`.