Match List I with List II LIST-I LIST-II (A) Torque (I) ML ^ -2 T… - Vidyadip

MCQ

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

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

✓

Answer

Correct option: C.

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

c
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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