# 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/cm3 and g = 10 m/s2 the minimum and maximum pressure as calculated by the student should be : (i) 16 N/m2, 40 N/m2 (ii) 32 N/m2, 80 N/m2 (iii) 640 N/m2,1600 N/m2 (iv) 3200 N/m2,8000 N/m2

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 = 240cm3

density = 8g/cm3

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 cm2 = 24x 10-4  m2

so,

P (largest) = F / A(smallest)

or

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

thus,

P(largest) = 8000 N/m2

.

now

largest A = 6cm x 10cm = 60 cm2 = 60x 10-4  m2

so,

P (smallest) = F / A(largest)

or

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

thus,

P(smallest) = 3200 N/m2

.

thus, the correct answer is option (iv)

3200 N/m2, 8000 N/m2

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