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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. The maximum weight that can be put on the block without wetting it is :

(Density of wood=800kg/m3 and spring constant of the spring =50N/m. Take g=10m/s2 )

25060_76dc904a4f1744e696c9b97c3b540c81.png

A
0.35N
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B
0.55N
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C
0.65N
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D
0.75N
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Solution

The correct option is A 0.35N
Density of the wood=800kg/m3
volume of cube =27cm3
weight of cube =0.8×27gms
=21.6gms
let height of cube dipped in water be h,
for equilibrium,
weight of water displaced= weight of cube
=9h×1000=21.6
h=21.69cms=2.4cms
let maximum weight on that can be put on the cube without actually wetting it is w
balancing the forces, w+21.6×101000=271000×10+50×0.6100
W=0.270.216+0.3
w=0.354N
W0.35N

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