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