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

Applying the principle of homogeneity of dimensions,determine which one is correct. Where $T$ is time period,$G$ is gravitational constant,$M$ is mass,and $r$ is the radius of the orbit.

The position of a particle moving on the $x-$axis is given by $x(t) = A \sin t + B \cos^2 t + Ct^2 + D$,where $t$ is time. The dimension of $\frac{ABC}{D}$ is $-$

If the formula is $X = 3 Y Z^{2}$,where $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively,then the dimensions of $Y$ in the $MKSQ$ system are:

Even if a physical quantity depends upon three quantities,out of which two are dimensionally same,then the formula cannot be derived by the method of dimensions. This statement

The foundations of dimensional analysis were laid down by

Vedclass Test Series

Exam Paper Generator

Online Exam Module