A wooden box of mass 2 kg and dimensions (30 cm $\times$ 15 cm $\times$ 10 cm) is placed on a table with sides 30 cm and 10 cm touching the tabletop. Which one of the following is the approximate pressure exerted on the table?
111.1 N/m$^2$
222.2 N/m$^2$
333.3 N/m$^2$
666.6 N/m$^2$
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2022
Assume acceleration due to gravity $g \approx 10$ m/s$^2$ for approximation, as is common in such problems.
Force (weight) $F = mg = 2 \text{ kg} \times 10 \text{ m/s}^2 = 20 \text{ N}$.
The dimensions of the box are 30 cm $\times$ 15 cm $\times$ 10 cm.
The box is placed with sides 30 cm and 10 cm touching the tabletop. The contact area is $A = (30 \text{ cm}) \times (10 \text{ cm})$.
Convert area to square meters: $A = (0.30 \text{ m}) \times (0.10 \text{ m}) = 0.03 \text{ m}^2$.
Pressure $P = F / A = 20 \text{ N} / 0.03 \text{ m}^2 = 20 / (3/100) \text{ N/m}^2 = (20 \times 100) / 3 \text{ N/m}^2 = 2000 / 3 \text{ N/m}^2$.
$2000 / 3 \approx 666.67 \text{ N/m}^2$.
Looking at the options, 666.6 N/m$^2$ is the closest value.
If $g = 9.8$ m/s$^2$ was used, $F = 2 \times 9.8 = 19.6$ N. $P = 19.6 / 0.03 = 1960 / 3 \approx 653.33$ N/m$^2$. 666.6 is still the closest option, suggesting $g=10$ m/s$^2$ was intended.