A student placed an iron cuboid of dimensions 4 cm * 6 cm * 10 cm on a tray containing fine sand. He placed the cuboid in such a way that it was made to lie on the sand with its faces of dimension (a) 4 cm x 6 cm (b) 6 cm x 10 cm (c) 4 cm x 10 cm.

If the density of iron is nearly 8 g/cm^{3} and g = 10 m/s^{2} the minimum and maximum pressure as calculated by the student should be :

(i) 16 N/m^{2}, 40 N/m^{2}

(ii) 32 N/m^{2}, 80 N/m^{2}

(iii) 640 N/m^{2},1600 N/m^{2}

(iv) 3200 N/m^{2},8000 N/m^{2}

we know that pressure is given as

P = F/A

so, P will be greatest for smallest value of A and smallest for the greatest value of A.

here,

F = weight of the block = mg = (density x volume) x g

volume = 4cm x 6cm x 10cm = 240cm^{3}

density = 8g/cm^{3}

so,

F = (240 x 8) x 1000

thus,

F = 1920000 dynes (this is in cgs units)

or in MKS units (as 1 dyne = 10^{-5} N)

F = 19.2 N

.

now

smallest A = 4cm x 6cm = 24 cm^{2} = 24x 10^{-4} m^{2}

so,

P (largest) = F / A(smallest)

or

P(largest) = 19.2 / 24x 10^{-4}

thus,

**P(largest) = 8000 N/m**^{2}

.

now

largest A = 6cm x 10cm = 60 cm^{2} = 60x 10^{-4} m^{2}

so,

P (smallest) = F / A(largest)

or

P(smallest) = 19.2 / 60 x 10^{-4}

thus,

**P(smallest) = 3200 N/m**^{2}

.

thus, the correct answer is option (iv)

3200 N/m^{2}, 8000 N/m^{2}

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