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Using dimensional analysis, determine which of the following pairs of physical quantities have the same dimensions?
Question

Using dimensional analysis, determine which of the following pairs of physical quantities have the same dimensions?

A.

Latent heat and gravitational potential

B.

Linear momentum and angular momentum

C.

Force and torque

D.

Work and power

Correct option is A

The correct option is: (a) Latent heat and gravitational potential

Explanation:

  • Latent heat and gravitational potential both have the dimension of energy per unit mass, i.e., [L²T⁻²].
  • Dimensional analysis shows that both represent energy-related quantities divided by mass.
Information Booster:
  • Latent Heat: Energy required per unit mass to change the state of a substance.
  • Gravitational Potential: Work done per unit mass to bring it from infinity to a point in space.
Additional Information:
  • Momentum: [MLT⁻¹]; angular momentum has extra rotational component.
  • Force: [MLT⁻²]; torque has unit [ML²T⁻²].
  • Work: [ML²T⁻²]; power = work/time = [ML²T⁻³].

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