1. Tardigrade
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  4. Which of the following pairs have same dimensional formula for both the quantities? (1) Kinetic energy and torque (2) Resistance and inductance (3) Young’s modulus and pressure

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Q. Which of the following pairs have same dimensional formula for both the quantities?
(1) Kinetic energy and torque
(2) Resistance and inductance
(3) Young’s modulus and pressure

Physical World, Units and Measurements

Solution:

Both kinetic energy and torque have same dimensional formula $\left[ ML ^{2} T ^{-2}\right]$. Resistance and inductance have different dimensional formulae. Dimensional formula of resistance is
$\left[ ML ^{2} T ^{-3} A ^{-2}\right]$.
Dimensional formula of inductance is
$\left[ ML ^{2} T ^{-2} A ^{-2}\right]$.
Both Young's modulus and pressure have same dimensional formula $\left[ ML ^{-1} T ^{-2}\right]$.