A block of wood 40 cm × 20 cm × 10 cm) is kept on a tabletop in three different positions: (a) with its side of dimensions 20 cm × 10 cm; (b) with its side of dimensions 10 cm × 40 cm; and (c) with its side of dimensions 40 cm × 20 cm. The pressure exerted by the wooden block on the tabletop in these positions is represented by P_A, P_B and P_c, respectively. The pressure follows the trend

Question

Question

This question was previously asked in

UPSC NDA-II (General Ability) Official Paper-I (Held On: 03 Sept, 2023)

Answer 1

The correct answer is PA > PB > Pc.

Key Points

The pressure exerted by an object on a surface is given by the formula:
- P = F/A
  - where:
  - P is the pressure,
  - F is the force applied perpendicular to the surface,
  - A is the area over which the force is applied.
In this case, the weight of the block (force) is constant, but the area over which the weight is distributed changes based on the orientation of the block.
- (a) P × A with side dimensions 20 cm × 10 cm:
  - A_A= 20 cm × 10 cm = 200 cm²
- (b) P × B with side dimensions 10 cm × 40 cm:
  - A_B= 10cm × 40 cm = 400 cm²
- (c) P × C with side dimensions 40 cm × 20 cm:
  - A_C = 40 cm × 20 cm = 800 cm²
Now, considering the pressure formula:
Therefore, the trend in pressure would be:
- PA > PB > Pc
So, the pressure exerted by the wooden block on the tabletop follows the trend PA > PB > Pc in these positions.