JEE Main 2023 — Units and Dimensions Question with Solution

Unit of force is written as, $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-2}$.

Now, torque can be written as, $\tau =Fs$ therefore its unit can be written as $\mathrm{kg} {\mathrm{m}}^2 {\mathrm{s}}^{–2}$.

Pressure is given by, $P=\frac{F}{A}$, therefore unit of pressure will be $\mathrm{kg} {\mathrm{m}}^{-1} {\mathrm{s}}^{-2}$.

Now, pressure gradient is given by ratio of pressure and distance, so its unit will be $\mathrm{kg} {\mathrm{m}}^{-2} {\mathrm{s}}^{-2}$.

Impulse is given by product of force and time, so its unit will be $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$.

As we know unit of torque and energy is the same, therefore energy density can written as $=\frac{\text{energy}}{\text{volume}}=\mathrm{kg} {\mathrm{m}}^{-1} {\mathrm{s}}^{–2}$.