JEE PYQ: Units & Measurements - Question ID 65a85ef90e19 (JEE Main 2022)

Core Formula & Concept:

In the chapter Units & Measurements, every physical quantity is expressed in terms of its dimensional formula and the corresponding SI unit. The key idea is to recall the SI unit of each quantity in List I and then match it with the unit given in List II.

• Torque ($\tau$): Defined as the cross product of force ($F$) and position vector ($r$). Its SI unit is newton-metre (Nm), which is dimensionally equivalent to $[M L^2 T^{-2}]$.
• Stress ($\sigma$): Defined as force per unit area. Its SI unit is newton per square metre (Nm^-2), also known as pascal (Pa).
• Latent Heat ($L$): Defined as the amount of heat energy ($Q$) required to change the phase of a unit mass ($m$) of a substance without changing its temperature. Its SI unit is joule per kilogram (J kg^-1).
• Power ($P$): Defined as the rate of doing work or the rate of energy transfer. Its SI unit is joule per second (J s^-1), which is equivalent to watt (W) or newton-metre per second (Nm s^-1).

Step-by-Step Derivation:

Step 1: Analyze List I and List II units

Step 2: Verify each match

• A. Torque → III. Nm ✔️
• B. Stress → IV. Nm^-2 ✔️
• C. Latent Heat → II. J kg^-1 ✔️
• D. Power → I. Nm s^-1 ✔️

Step 3: Compare with given options

The derived matches are:

• A-III
• B-IV
• C-II
• D-I

This corresponds exactly to Option B. Common Traps & Exam Tip:

Students often confuse the units of torque and work/energy, both of which have the unit Nm. However, torque is a vector quantity, while work/energy is scalar. In this question, the unit Nm is correctly matched with torque (A-III), not with latent heat or power.

Another common mistake is misidentifying the unit of power. Students sometimes confuse it with energy (J) or work (Nm), but power is energy per unit time (J s^-1 or Nm s^-1), which matches I. Nm s^-1.

Exam Tip: Always recall the definition of each physical quantity and its SI unit before matching. Avoid relying on memory alone—derive the units from fundamental definitions when in doubt.