Which of the following expressions can be ded | vedclass

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(C) Dimensional analysis is a powerful tool for checking the consistency of physical equations,but it has limitations. It cannot determine dimensionle

Vedclass · Accepted Answer

$F=6 \pi \eta r 
u$

Vedclass · Answer

(C) Dimensional analysis is a powerful tool for checking the consistency of physical equations,but it has limitations. It cannot determine dimensionless constants (like $6 \pi$) or the presence of transcendental functions (like trigonometric,exponential,or logarithmic functions) because their arguments must be dimensionless.$1$. $x=A \cos (\omega t)$: While dimensionally consistent,the presence of the trigonometric function $\cos$ cannot be derived using dimensional analysis.$2$. $N=N_0 e^{-\lambda t}$: While dimensionally consistent,the exponential form cannot be derived using dimensional analysis.$3$. $F=6 \pi \eta r 
u$ (Stokes' Law): The dimensions of the right-hand side are $[M L^{-1} T^{-1}] \cdot [L] \cdot [L T^{-1}] = [M L T^{-2}]$,which is the dimension of force. Dimensional analysis can relate $F$ to $\eta$,$r$,and $
u$ as $F \propto \eta^a r^b 
u^c$. By comparing dimensions,we can find $a=1, b=1, c=1$,leading to $F \propto \eta r 
u$. Thus,the functional dependence can be deduced.Therefore,option $C$ is the correct choice.

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

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