The pairs of physical quantities that have the same dimensions is (are) :
Answers: A. Reynolds number and coefficient of friction · B. Curie and frequency of a light wave · C. Latent heat and gravitational potential
Or read the worked solution below. Jump to the steps ↓
Written solution
Step 1: Analyze Pair (1) — Reynolds number and coefficient of friction.
The Reynolds number is defined as:
Since all units cancel out, it is dimensionless:
The coefficient of friction is the ratio of two forces:
Both quantities are dimensionless, so they have the same dimensions.
Step 2: Analyze Pair (2) — Curie and frequency of a light wave.
Curie is a unit of radioactivity representing decay rate per unit time:
The frequency of a light wave is:
Both quantities have the same dimension of inverse time.
Step 3: Analyze Pair (3) — Latent heat and gravitational potential.
Latent heat is heat energy per unit mass:
Gravitational potential is work done per unit mass:
Both quantities have the same dimensions.
Step 4: Analyze Pair (4) — Planck's constant and torque.
Planck's constant is defined via energy and frequency:
Torque is defined as force times perpendicular distance:
These two quantities have different dimensions.
Answer: The pairs of physical quantities that have the same dimensions are (1) Reynolds number and coefficient of friction, (2) Curie and frequency of a light wave, and (3) Latent heat and gravitational potential.