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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Options

A. `a(a^(2)rhog+K)`
B. `a(arhog+2K)`
C. `a((arhog)/2+2K)`
D. `a(a^(2)rhog+K/2)`

Answer

D

Explanation

Since density of block `=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 futher immersed in water.
Therefore `W=` Extra uptrust `+` Spring force
`=axxaxxa/2xx2rhoxxg+K(a/2)`
`=a(a^(2)rhog+K/2)`