Units & Dimensions

JEE Main level, single correct, medium

8 of 149

Question 8 of 149

Match List I with List II List I List II A Torque I kgm–1s–2kg{m}^{–1}{s}^{–2} B Energy density II kgms–1kgm{s}^{–1} C Pressure gradient III kgm–2s–2kg{m}^{–2}{s}^{–2} D Impulse IV kgm2s–2kg{m}^{2}{s}^{–2} Choose the correct answer from the options given below :

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Answer: (D) A-IV, B-I, C-III, D-II

Unit of force is written as, kgms−2kgm{s}^{-2}.
Now, torque can be written as, τ=Fs\tau =Fs therefore its unit can be written as kgm2s–2kg{m}^{2}{s}^{–2}.
Pressure is given by, P=FAP=\dfrac{F}{A}, therefore unit of pressure will be kgm−1s−2kg{m}^{-1}{s}^{-2}.
Now, pressure gradient is given by ratio of pressure and distance, so its unit will be kgm−2s−2kg{m}^{-2}{s}^{-2}.
Impulse is given by product of force and time, so its unit will be kgms−1kgm{s}^{-1}.
As we know unit of torque and energy is the same, therefore energy density can written as =energyvolume=kgm−1s–2=\dfrac{\text{energy}}{\text{volume}}=kg{m}^{-1}{s}^{–2}.

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