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Which of the following pairs of units are used for measuring the same physical quantity ?

  • A.\(\text{kg m/s}^{2}\), Nm
  • B.\(\text{kg m}^{2}\text{/s}^{2}\), Ws
  • C.\(\text{kg m/s}^{2}\), Ws
  • D.\(\text{kg m}^{2}\text{/s}^{2}\), J/s

Answer: B

The pair is \(\text{kg m}^{2}\text{/s}^{2}\) and Ws; both measure energy (work).

Work = force × distance, so its unit is N m = (kg m/s²) × m = kg m²/s², which is the joule. Energy is also power × time, so a watt-second is a joule too.

The other pairs mix quantities: kg m/s² is the newton, a unit of force, while N m and W s are units of energy; and J/s is the watt, a unit of power, not energy.

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