Match List I with List II: List I (Physical Quantity) List II (Dimensional Formula) (A) Pressure gradient (I) [ M 0 L 2 T -2 ] (B) Energy density (II) [ M 1 L -1 T -2 ] (C) Electric Field (III) [ M 1 L -2 T -2 ] (D) Latent heat (IV) [ M 1 L 1 T -3 A -1 ] Choose the correct answer from the options given below:

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

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

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

JEE Mains · Physics · STD 11 - Units,dimensions and measurement

Match List \(I\) with List \(II\) :

List \(I\) (Physical Quantity) List \(II\) (Dimensional Formula)

\((A)\) Pressure gradient \((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)

\((B)\) Energy density \((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)

\((C)\) Electric Field \((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)

\((D)\) Latent heat \((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below:

Pick an option to check your answer.

Verified Solution

Correct Answer

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

Detailed explanation

Pressure gradient\(=\frac{ dp }{ dx }=\frac{\left[ ML ^{-1} T ^{-2}\right]}{[ L ]}\)

\(=\left[ M ^1 L ^{-2} T ^{-2}\right]\)

Energy density \(=\frac{\text { energy }}{\text { volume }}=\frac{\left[ ML ^2 T ^{-2}\right]}{\left[ L ^3\right]}\)

\(=\left[ M ^1 L ^{-1} T ^{-2}\right]\)

\(\text { Electric field }=\frac{\text { Force }}{\text { ch arge }}=\frac{\left\lfloor MLT ^{-2}\right\rfloor}{[ A . T ]}\)

\(=\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

\(\text { Latent heat }=\frac{\text { heat }}{\text { mass }}=\frac{\left[ ML ^2 T ^{-2}\right]}{[ M ]}\)

\(=\left[ M ^0 L ^2 T ^{-2}\right]\)

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