A student placed an iron cuboid of dimensions 1cm x 4cm x 10cm on the loose sand with its

dimensions (a) 1cm x 4cm  (b) 4cm x 10cm lie on the sand. If the pressures exerted by the cuboid in

two cases are P1 and P2 respectively, then calculate P1/P2.

Dear student,

The volume of the cuboid will be 
= 1cm x 4cm x 10cm
=40 cm³

If the density of iron is nearly 8 g/cm³ and g = 10 m/s² 

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

= (40 x 8) x 1000
= 320000 dynes (this is in cgs units)

or in MKS units (as 1 dyne = 10^-5 N)

F = 3.2 N

The pressure is given as 

P = F/A

​​​​​For (a) 1cm x 4cm
Then, 
pressure = force / area 
P₁= $\frac{3.2}{4\times 1}=0.8$ N/cm²
For, (b) 4cm x 10cm
P₂ = $\frac{3.2}{4\times 10}=0.08$ N/cm²
Therefore,

$\frac{P_1}{P_2}=\frac{0.8}{0.08}=$10