NDA (II) 2016 General Ability Test · Question 76 of 150

Correct — C, the ratio of the component of force normal to the area to that area. Pressure is defined using only the part of the force that acts perpendicular to a surface. Once the surface is fixed, that perpendicular direction is already settled by the surface itself, so the normal component is just a number; dividing it by the area leaves a quantity with size but no direction of its own, which is exactly what a scalar is. The physical check is Pascal's observation that pressure at a point inside a fluid at rest pushes equally in every direction — a quantity that acts the same way in all directions cannot be carrying a direction.

• (a)it is the ratio of force to area and both force and area are vectors — Dividing one vector by another is not a defined operation in physics, so this cannot be anybody's definition of pressure. Area can be given a vector character through its outward normal, but that only strengthens the case for reading pressure as force dotted with the normal — it never makes a vector-by-vector division legitimate.
• (b)it is the ratio of magnitude of force to area — The tempting near-miss, and the option most candidates mark. Taking the magnitude of the whole force would sweep in any part of the force that slides along the surface, and that tangential part is shear stress, not pressure. The definition has to pick out the normal component first, which is what option (c) does.
• (d)none of the above — Option (c) is a complete and correct statement of the definition, so there is nothing left for a catch-all option to cover.

Pressure is the normal force per unit area — the force component perpendicular to a surface divided by the area of that surface. Its SI unit is the pascal, one newton per square metre. A scalar is a quantity fully described by a magnitude alone, and pressure qualifies because the surface, not the pressure, supplies the direction. The same logic makes work a scalar even though it is built out of two vectors, force and displacement.

The trap in this item is the instinct that a quantity assembled from vectors must itself be a vector. It need not be. The real discrimination is between options (b) and (c): both look like force divided by area, but only (c) says which part of the force counts. Split any force acting on a surface into a normal push and a tangential drag; the normal push per unit area is pressure, the tangential drag per unit area is shear stress, and a fluid at rest can sustain the first but not the second.

• Pressure is normal force per unit area; the SI unit is the pascal, equal to one newton per square metre.
• One standard atmosphere is 101,325 pascals and one bar is exactly 100,000 pascals.
• In a fluid at rest the pressure at a point is the same in every direction, which is Pascal's law.
• The tangential force per unit area on a surface is a separate quantity called shear stress, and a fluid at rest cannot support it.

• Assuming that any quantity built out of vectors must itself be a vector — work and pressure are both counter-examples.
• Treating the whole force divided by area as pressure, which quietly includes the shear part.

NDA runs a steady supply of one-line scalar-or-vector items, and likes to place two nearly identical definitions side by side, so read every option to its last word before marking.

• practice — not a real PYQ

  Which one of the following is a vector quantity?

  • (a)Work
  • (b)Pressure
  • (c)Impulse
  • (d)Energy

  Answer(c) Impulse — it equals force multiplied by time, so it keeps the direction of the force; work, pressure and energy are all scalars.

• practice — not a real PYQ

  The force per unit area acting parallel to a surface is called

  • (a)pressure
  • (b)shear stress
  • (c)thrust
  • (d)surface tension

  Answer(b) shear stress — pressure uses only the perpendicular component of the force.