A cuboid has dimension 4 cm × 7 cm × 10 cm. It is placed on the sand. The density of the material of the cuboid is 8 g/cm3. The cuboid is placed on the sand in such a way that there is minimum pressure on the sand. The value of minimum pressure is ____ N/m2. Take g = 10 m/s2.

Question

A cuboid has dimension 4 cm × 7 cm × 10 cm. It is placed on the sand. The density of the material of the cuboid is 8 g/cm3. The cuboid is placed on the sand in such a way that there is minimum pressure on the sand. The value of minimum pressure is ____ N/m2. Take g = 10 m/s2.

Accepted Answer

A cuboid has dimension 4 cm × 7 cm × 10 cm. It is placed on the sand. The density of the material of the cuboid is 8 g/cm3. The cuboid is placed on the sand in such a way that there is minimum pressure on the sand. The value of minimum pressure is 3200 Nm2.Step-1: Finding the weight of the cuboidVolume of cuboid  = 4 × 7 × 10 cm3 Volume of cuboid = 280 cm3Density of the material of the cuboid is given = 8 g/cm3The formula for density is given asDensity=MassVolume⇒Mass=Density ×VolumeSubstituting the values⇒Mass=8 ×280 g⇒Mass=2240 g⇒Mass=2.24 kgWeight of the cuboid is given asW=mgWhere m = mass of the cuboid = 2.24 kg            g = Acceleration due to gravity = 10 m/s2Putting the values    W=2.24 ×10⇒W=22.4 NStep-2: Calculating the minimum pressureThe formula for pressure is given as                                                P=ForceAreaHere, the value of force is equal to the weight of the cuboidSo, to minimize the pressure we need maximum area. The face which has the maximum area is the face with the dimension of  7 cm × 10 cm Area = 70 cm2 = 0.007 m2Minimum Pressure = 22.40.007 N/m2Minimum Pressure = 3200 N/m2Hence, the value of minimum pressure is 3200 N/m2.

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