A, B, C and D are four different physical qua | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In the equation $AD = C \ln(BD)$,the argument of the logarithmic function must be dimensionless. Therefore,the dimension of $BD$ must be $1$ (dime

Vedclass · Accepted Answer

$\frac{A - C}{D}$

Vedclass · Answer

(D) In the equation $AD = C \ln(BD)$,the argument of the logarithmic function must be dimensionless. Therefore,the dimension of $BD$ must be $1$ (dimensionless),i.e.,$[BD] = [M^0 L^0 T^0]$.This implies $[B] = [D]^{-1}$.Substituting this into the equation,we have $[AD] = [C] 	imes [1]$,so $[A][D] = [C]$.For a physical quantity to be meaningful in addition or subtraction,the dimensions of the terms must be identical.Checking option $D$: $\frac{A - C}{D}$. Here,$A$ and $C$ are being subtracted. Since $[A] = [C][D]^{-1}$ and $[C] = [A][D]$,the dimensions of $A$ and $C$ are different. Thus,$A - C$ is not a meaningful operation.

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. We know that the equation $AD = C \ln(BD)$ holds true. Which of the following combinations is not a meaningful quantity?

Similar Questions

If the dimensions of $A$ and $B$ are different,which of the following operations is physically meaningful?

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

$A$ quantity $z$,to be estimated,has a dependency on the variables $a, b$ and $c$ as $z = a b^2 c^{-2}$. The percentage errors in the measurement of $a, b$ and $c$ are $2.1 \%$,$1.3 \%$ and $2.2 \%$,respectively. The percentage error in the measurement of $z$ would then be: (in $\%$)

If the charge of electron $e$,mass of electron $m$,speed of light in vacuum $c$,and Planck's constant $h$ are taken as fundamental quantities,then the permeability of vacuum $\mu_0$ can be expressed as

Vedclass Test Series

Exam Paper Generator

Online Exam Module