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1.Units, Dimensions and Measurement
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सूची $I$ का सूची $II$ के साथ मिलान करें।
| सूची-$I$ | सूची-$II$ |
| $A$ बल आघूर्ण | $I$ $\mathrm{ML}^{-2} \mathrm{~T}^{-2}$ |
| $B$ प्रतिबल | $II$ $\mathrm{ML}^{-2} \mathrm{~T}^{-2}$ |
| $C$ दाब प्रवणता | $III$ $\mathrm{ML}^{-1} \mathrm{~T}^{-1}$ |
| $D$ श्यानता गुणांक | $IV$ $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$ |
A$(A)-(III), (B)-(IV), (C)-(I), (D)-(II)$
B$(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$
C$(A)-(II), (B)-(IV), (C)-(I), (D)-(III)$
D$(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$
(JEE MAIN-2023)
Solution
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 $\Rightarrow F=6 \pi \eta rV$
$MLT ^{-2}=[\eta] L ^2 T ^{-1}$
${[\eta]= ML ^{-1} T ^{-1}}$
${[\tau]=[ L ]\left[ MLT ^{-2}\right] }$
$\Rightarrow ML ^2 T ^{-2}$
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 $\Rightarrow F=6 \pi \eta rV$
$MLT ^{-2}=[\eta] L ^2 T ^{-1}$
${[\eta]= ML ^{-1} T ^{-1}}$
Standard 11
Physics
