If momentum [P],area [A],and time [T] are tak | vedclass

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

Question

(A) The dimensional formula for the coefficient of viscosity $\eta$ is $[M^1 L^{-1} T^{-1}]$.Let the dimensional formula be expressed as $\eta = P^x A

Vedclass · Accepted Answer

$[PA^{-1}T^0]$

Vedclass · Answer

(A) The dimensional formula for the coefficient of viscosity $\eta$ is $[M^1 L^{-1} T^{-1}]$.Let the dimensional formula be expressed as $\eta = P^x A^y T^z$.We know the dimensions of the fundamental quantities are:$[P] = [M^1 L^1 T^{-1}]$$[A] = [L^2]$$[T] = [T^1]$Substituting these into the equation:$[M^1 L^{-1} T^{-1}] = [M^1 L^1 T^{-1}]^x [L^2]^y [T^1]^z$$[M^1 L^{-1} T^{-1}] = M^x L^{x+2y} T^{-x+z}$Comparing the powers of $M, L,$ and $T$ on both sides:For $M: x = 1$For $L: x + 2y = -1 \implies 1 + 2y = -1 \implies 2y = -2 \implies y = -1$For $T: -x + z = -1 \implies -1 + z = -1 \implies z = 0$Thus,the dimensional formula is $[P^1 A^{-1} T^0]$.

If momentum $[P]$,area $[A]$,and time $[T]$ are taken as fundamental quantities,then the dimensional formula for the coefficient of viscosity is:

Similar Questions

In the expression $A=B+\frac{C}{D+E}$,the dimensions of physical quantities $B$ and $C$ are $[L^{1} M^{0} T^{-1}]$ and $[L^{1} M^{0} T^{0}]$ respectively. The dimensions of quantities $A, D$ and $E$ are

The refractive index of the medium is $\mu = A + \frac{B}{\lambda^{2}}$,where $A$ and $B$ are constants and $\lambda$ is the wavelength of light. The dimensions of $B$ are the same as that of

The formula is $X = 5YZ^2$,where $X$ and $Z$ have dimensions of capacitance and magnetic field,respectively. What are the dimensions of $Y$ in $SI$ units?

The electric field in a certain region is given by the formula $\vec{E} = (\frac{K}{x^3}) \hat{i}$. What is the dimensional formula of $K$?

$1$ joule of energy is to be converted into a new system of units in which length is measured in $10 \,m$,mass in $10 \,kg$,and time in $1 \,minute$. The numerical value of $1 \,J$ in the new system is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module