A hammer exerts a force of 1.5 N on each of the two nails A and B. The area of cross section of tip of nail A is 2 mm² while that of nail B is 6 mm² . Calculate pressure on each nail in pascal.

As we know,

Pressure (P) = $\dfrac{\text {Thrust (F)}}{\text {Area (A)}}$

Given,

F = 1.5 N

A = 2 mm²

Converting 2 mm² in metre²

As 1 mm = $\dfrac{1}{1000}$ m

So, 1 mm² = (1) mm x (1) mm

= $(\dfrac{1}{1000}) m \times (\dfrac{1}{1000}) m$

= 1 x 10 ^-6 m²

Hence,

2 mm² = 2 x 10^-6 m²

A_A = 2 x 10 ^-6 m²

A_B = 6 x 10 ^-6 m²

Substituting the values in the formula above, we get,

Pressure on A

$P = \dfrac{1.5}{2 \times 10^{-6}} \\[0.5em] P = 0.75 \times 10^{6} \\[0.5em] \Rightarrow P = 7.5 \times 10^{5} Pa \\[0.5em]$

Hence, Pressure on A = 7.5 x 10⁵ Pa

Pressure on B

$P = \dfrac{1.5}{6 \times 10^{-6}} \\[0.5em] P = 0.25 \times 10^{6} \\[0.5em] \Rightarrow P = 2.5 \times 10^{5} Pa \\[0.5em]$

Hence, Pressure on B = 2.5 x 10⁵ Pa