NDA (II) 2016 General Ability Test · Question 81 of 150

Correct — B, an acceleration of 1 m/s². Newton's second law gives force as mass times acceleration, so acceleration is force divided by mass. Putting in the numbers, 1 newton divided by 1 kilogram gives 1 metre per second squared. This is not a coincidence but the definition of the unit: the newton was created precisely as the force that gives a one-kilogram mass an acceleration of one metre per second squared, so 1 N is exactly 1 kg m/s². A steady force on a freely movable body produces a steady acceleration, meaning the speed keeps growing — after one second the body is moving at 1 m/s, after two seconds at 2 m/s, and so on.

• (a)speed of 1 km/s — Wrong on both counts. A constant force does not fix a speed, it fixes an acceleration, and the numerical value is a thousand times too large because it uses kilometres where the definition of the newton uses metres.
• (c)speed of 1 m/s — The main trap, because the number 1 and the metre look right. But a force applied to a body free to move never settles it at a fixed speed — it keeps changing the speed for as long as it acts. Only if the body were already moving and the net force were zero would the speed stay constant, which is Newton's first law rather than the second.
• (d)acceleration of 1 km/s² — The right physical quantity with the wrong unit. One kilometre per second squared is a thousand metres per second squared, so this overstates the answer by a factor of a thousand — an acceleration around a hundred times that of free fall from a force of just one newton.

Newton's second law of motion states that the net force on a body equals the rate of change of its momentum, which for constant mass reduces to force equals mass times acceleration. Acceleration therefore equals force divided by mass, and mass is the constant of proportionality — the measure of how strongly a body resists being accelerated. The SI unit of force, the newton, is defined from this relation as the force needed to accelerate one kilogram at one metre per second squared.

The whole item turns on knowing that force controls acceleration, not speed, and then on reading the unit carefully. Two of the four options offer a speed and two offer an acceleration, and within each pair one is in metres and one in kilometres, so the examiner is testing two things at once with a single number. A quick sanity check is that 1 m/s² is a very gentle acceleration, roughly a tenth of free fall, which is what one expects from a one-newton push on a one-kilogram object — about the weight of a medium apple. If the answer had come out in kilometres per second squared, that alone should have looked absurd.

• One newton equals one kilogram metre per second squared, and it is defined as the force that accelerates a 1 kg mass at 1 m/s².
• Newton's second law in its general form says force equals the rate of change of momentum; force equals mass times acceleration follows when the mass is constant.
• A constant net force produces a constant acceleration, so the velocity changes steadily rather than settling at a fixed value.
• Zero net force means zero acceleration, which is a body at rest or moving with constant velocity — Newton's first law.

• Reading a force as producing a fixed speed rather than a steady acceleration.
• Missing the unit switch between metres and kilometres inside otherwise identical options.

NDA likes definition-of-the-unit items — the newton, the joule, the pascal, the watt — dressed up as small numerical questions, so learn each unit as the physical situation that produces exactly one of it.

• practice — not a real PYQ

  A net force of 10 N acts on a body of mass 2 kg that is free to move. The acceleration produced is

  • (a)0.2 m/s²
  • (b)5 m/s²
  • (c)20 m/s²
  • (d)12 m/s²

  Answer(b) 5 m/s² — acceleration is force divided by mass, so 10 N divided by 2 kg gives 5 m/s².

• practice — not a real PYQ

  One newton is equivalent to

  • (a)1 kg m/s
  • (b)1 kg m/s²
  • (c)1 kg m²/s²
  • (d)1 kg/m s²

  Answer(b) 1 kg m/s² — the newton is defined from force equals mass times acceleration.