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Question

(A) The dimensional formulas for the given physical quantities are:$1$. Angular momentum $(L = mvr)$: Dimensions are $[M][LT^{-1}][L] = [ML^2T^{-1}]$.

Vedclass · Accepted Answer

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

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(A) The dimensional formulas for the given physical quantities are:$1$. Angular momentum $(L = mvr)$: Dimensions are $[M][LT^{-1}][L] = [ML^2T^{-1}]$. Thus, $(A)-(I)$.$2$. Torque $(	au = r 	imes F)$: Dimensions are $[L][MLT^{-2}] = [ML^2T^{-2}]$. Thus, $(B)-(II)$.$3$. Stress $(\sigma = 	ext{Force} / 	ext{Area})$: Dimensions are $[MLT^{-2}] / [L^2] = [ML^{-1}T^{-2}]$. Thus, $(C)-(III)$.$4$. Pressure gradient $(\Delta P / \Delta x)$: Dimensions are $[ML^{-1}T^{-2}] / [L] = [ML^{-2}T^{-2}]$. Thus, $(D)-(IV)$.Therefore, the correct matching is $(A)-(I), (B)-(II), (C)-(III), (D)-(IV)$.

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

List-$I$	List-$II$
$A$. Coefficient of viscosity	$I$. $[ML^{-1}T^{-2}]$
$B$. Surface tension	$II$. $[ML^2T^{-2}]$
$C$. Pressure	$III$. $[ML^0T^{-2}]$
$D$. Surface energy	$IV$. $[ML^{-1}T^{-1}]$

Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$

$(B)$ Torque $(II)$ $[ML^2T^{-2}]$

$(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$

$(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$

Choose the correct answer from the options given below:

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Match List-$I$ with List-$II$.
List-$I$ List-$II$
$A$. Coefficient of viscosity $I$. $[ML^{-1}T^{-2}]$
$B$. Surface tension $II$. $[ML^2T^{-2}]$
$C$. Pressure $III$. $[ML^0T^{-2}]$
$D$. Surface energy $IV$. $[ML^{-1}T^{-1}]$

Choose the correct answer from the options given below:

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Match List-$I$ with List-$II$. List-$I$ List-$II$ $(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$ $(B)$ Torque $(II)$ $[ML^2T^{-2}]$ $(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$ $(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$ Choose the correct answer from the options given below: