1. A cubical block of wood of edge 3 cm floats in water. The
louer surface of the cube just louches the free end of a vertical
a söring fixed at the bottom of the pol. The maximum weight that
can be put on the block without wetting it is (density of wood
= 800 kg/m and spring constant of the spring = 50 N/m. Take
g= 10 m/s)
20
Answers
The specific gravity of the block = 0.8.
Hence the height inside water = 3 cm × 0.8 = 2.4 cm.
The height outside ater = 3 cm - 2.4 = 0.6 cm. Suppose the maximum weight that can be put without wetting it is W.
The block in this case is completely immersed in the water. The volume of the displaced water
= volume of the block = 27 × 10-6 m3 .
Hence, the force of buoyancy = (27 × 10-6 m3) × 1(1000 kg/m3) × (10 m/s2) = 0.27 N.
The spring is compressed by 0.6 cm and hence the upward force exerted by the spring = 50 N/m × 0.6 cm = 0.3 N.
The force of buoyancy and the spring force taken together balance the weight of the block plus the weight W put on the block.
The weight of the block is W' = (27 × 10-6 m) × (800 kg/m3) × (10 m/s2) = 0.22 N. Thus, W = 0.27 N + 0.3 N - 0.22 N = 0.35 N.
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