NDA (II) 2023 General Ability Test · Question 112 of 146

Correct — A, P_A > P_B > P_C. Pressure is force divided by the area over which the force acts. Turning the block from one face to another does not change its weight, so the numerator stays fixed and the whole comparison is decided by the contact area. The three faces measure 20 cm × 10 cm = 200 cm², 10 cm × 40 cm = 400 cm² and 40 cm × 20 cm = 800 cm². Since pressure varies inversely with area, the smallest face gives the largest pressure, and the three values stand in the ratio 4 : 2 : 1. Hence P_A > P_B > P_C, and no numerical value of the block's mass is needed to say so.

• (b)P_A < P_B < P_C — This reverses the relationship. It would be right only if pressure rose with contact area, whereas pressure is weight divided by area, so a larger face spreads the same weight more thinly.
• (c)P_A = P_B = P_C — Equal pressures would require equal contact areas. The three faces are 200 cm², 400 cm² and 800 cm², all different, so the pressures cannot be equal. What is equal in all three positions is the total downward force, not the pressure.
• (d)P_A < P_B = P_C — It gets the direction of the first inequality wrong and also treats the last two as equal. The 10 cm × 40 cm face is 400 cm² and the 40 cm × 20 cm face is 800 cm² — a factor of two apart — so P_B is twice P_C, not equal to it.

Pressure is the force acting normally on a surface divided by the area of that surface, measured in pascals, where one pascal is one newton per square metre. A solid block resting on a table presses down with a force equal to its weight, however it is turned. So for one block on one table the only variable is which face is in contact, and pressure and contact area move in opposite directions.

The item is designed so that arithmetic is unnecessary — no mass is given and none is needed. Read off the three contact areas, notice that they are 200, 400 and 800 square centimetres, and the ordering follows. The tempting error is to reason from the height of the block or from how 'stable' each position looks, neither of which enters the formula. One presentation quirk is worth flagging so it does not distract: the stem labels the three positions (a), (b) and (c) in lower case and then names the pressures P_A, P_B and P_C in upper case; they are the same three positions in the same order.

• Pressure equals force divided by area; the SI unit is the pascal, equal to one newton per square metre.
• The weight of the block is the same in every position, so the force pressing on the table does not change.
• The three contact faces measure 200 cm², 400 cm² and 800 cm², so the pressures are in the ratio 4 : 2 : 1.
• This is why a sharp knife cuts better than a blunt one and why wide tracks stop a heavy vehicle sinking — the same force spread over a different area.

• Assuming a taller stack presses harder; height changes nothing for a solid block, only contact area does.
• Reaching for the mass of the block — the comparison is settled by ratios alone.
• Mixing up force and pressure; the force on the table is identical in all three positions.

Asked as a ratio-only comparison — three orientations of one object, order the pressures without computing any of them.

• practice — not a real PYQ

  A brick is placed on sand first on its largest face and then on its smallest face. Compared with the first case, in the second case the brick will

  • (a)exert a smaller pressure and sink less
  • (b)exert a greater pressure and sink more
  • (c)exert the same pressure and sink equally
  • (d)exert a greater force and sink more

  Answer(b) exert a greater pressure and sink more — the weight is unchanged, but the smaller contact area concentrates it, raising the pressure.

• practice — not a real PYQ

  A block of weight 40 N rests on a table with a contact face of area 0.02 m². The pressure exerted on the table is

  • (a)0.8 Pa
  • (b)20 Pa
  • (c)800 Pa
  • (d)2000 Pa

  Answer(d) 2000 Pa — pressure is force divided by area, 40 N ÷ 0.02 m² = 2000 N/m².