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

LIST\(-I\) LIST\(-II\)

\((A)\) Torque \((I)\) \(ML ^{-2} T ^{-2}\)

\((B)\) Stress \((II)\) \(ML ^2 T ^{-2}\)

\((C)\) Pressure of gradient \((III)\) \(ML ^{-1} T ^{-1}\)

\((D)\) Coefficient of viscosity \((IV)\) \(ML ^{-1} T ^{-2}\)

Choose the correct answer from the options given below

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

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

Detailed explanation

A. Torque \(\Rightarrow \vec{\tau}=\overrightarrow{ r } \times \overrightarrow{ F }\)

\({[\tau]=[ L ]\left[ MLT ^{-2}\right] }\)

\(\Rightarrow ML ^2 T ^{-2}\)

B. Stress \(=\frac{F}{A} \Rightarrow \frac{M L T^{-2}}{ L ^2}\)

\([\text { stress }]= ML ^{-1} T ^{-2}\)

C.\(\text { Pressure gradient }=\frac{\Delta P }{\Delta X }\)

\(\Rightarrow \frac{[ F / A ]}{[ L ]} \Rightarrow \frac{ ML T ^{-2}}{ L ^3}\)

\(\Rightarrow ML ^{-2} T ^{-2}\)

D. Coefficient of viscosity \(\Rightarrow F=6 \pi \eta rV\)

\(MLT ^{-2}=[\eta] L ^2 T ^{-1}\)

\({[\eta]= ML ^{-1} T ^{-1}}\)

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