A cubical block of wood of edge 3 cm floats in water.
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 kg/m 3 and spring
constant of the spring - 50 Wm. Take g = 10 m/s 2.
1 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.