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JEE MAIN - Physics (2023 - 8th April Evening Shift - No. 16)

Match List I with List II

LIST I LIST II
A. Torque I. $$\mathrm{ML^{-2}T^{-2}}$$
B. Stress II. $$\mathrm{ML^2T^{-2}}$$
C. Pressure gradient III. $$\mathrm{ML^{-1}T^{-1}}$$
D. Coefficient of viscosity IV. $$\mathrm{ML^{-1}T^{-2}}$$

Choose the correct answer from the options given below:

A-II, B-I, C-IV, D-III
A-II, B-IV, C-I, D-III
A-IV, B-II, C-III, D-I
A-III, B-IV, C-I, D-II

Explanation

Let's analyze the SI units of each quantity from List I:

  1. Torque: Torque (τ) is given by the cross product of the radius (r) and the force (F). Therefore, its SI units are Newton meter (Nm), which translates to $$\mathrm{ML^2T^{-2}}$$ in fundamental units.


  2. Stress: Stress is force per unit area. The SI unit for force is the Newton (N) and for area is meter squared (m²). Therefore, the SI unit for stress is Pascal (Pa), which translates to $$\mathrm{ML^{-1}T^{-2}}$$ in fundamental units.


  3. Pressure gradient: The pressure gradient is the rate of increase or decrease in pressure. It has units of pressure per distance. In SI units, that's Pascal per meter (Pa/m), which translates to $$\mathrm{ML^{-2}T^{-2}}$$ in fundamental units.


  4. Coefficient of viscosity: This is a measure of a fluid's resistance to shear or flow, and its SI units are the Pascal second (Pa.s), which translates to $$\mathrm{ML^{-1}T^{-1}}$$ in fundamental units.

Therefore, the correct matches are:

A - II B - IV C - I D - III

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