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(A) Step $1$: Analyze Assertion $A$. The dimensions of Pressure $(P)$ are $[M L^{-1} T^{-2}]$ and Time $(t)$ is $[T]$. Therefore,the dimension of $Pt$

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Both $A$ and $R$ are true,and $R$ is the correct explanation of $A$.

Vedclass · Answer

(A) Step $1$: Analyze Assertion $A$. The dimensions of Pressure $(P)$ are $[M L^{-1} T^{-2}]$ and Time $(t)$ is $[T]$. Therefore,the dimension of $Pt$ is $[M L^{-1} T^{-2}] 	imes [T] = [M L^{-1} T^{-1}]$.Step $2$: Analyze the dimension of the coefficient of viscosity $(\eta)$. From Newton's law of viscosity,$F = \eta A \frac{dv}{dx}$,so $\eta = \frac{F}{A (dv/dx)}$. The dimensions are $[M L T^{-2}] / ([L^2] 	imes [T^{-1}]) = [M L^{-1} T^{-1}]$. Thus,Assertion $A$ is true.Step $3$: Analyze Reason $R$. The formula for the coefficient of viscosity is $\eta = \frac{F}{A (dv/dx)}$. The statement provided in the original question was incomplete as it omitted the area term. With the correction,Reason $R$ is true and explains the dimension of viscosity. Therefore,both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

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