If z = xP + G,where P is pressure and G is th | vedclass

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

Question

(C) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.Given the equation $z = xP + G

Vedclass · Accepted Answer

$M^{-2} L^4 T^0, M^{-1} L^3 T^{-2}$

Vedclass · Answer

(C) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.Given the equation $z = xP + G$,it implies that $[z] = [xP] = [G]$.First,find the dimensions of $G$ (universal gravitational constant):$[G] = \frac{[F][r^2]}{[m_1][m_2]} = \frac{[MLT^{-2}][L^2]}{[M][M]} = [M^{-1} L^3 T^{-2}]$.Since $[z] = [G]$,the dimension of $z$ is $[M^{-1} L^3 T^{-2}]$.Next,find the dimensions of $P$ (pressure):$[P] = \frac{[Thrust]}{[Area]} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1} T^{-2}]$.Since $[z] = [xP]$,we have $[x] = \frac{[z]}{[P]} = \frac{[M^{-1} L^3 T^{-2}]}{[ML^{-1} T^{-2}]} = [M^{-2} L^4 T^0]$.Therefore,the dimensions of $x$ and $z$ are $[M^{-2} L^4 T^0]$ and $[M^{-1} L^3 T^{-2}]$ respectively.

If $z = xP + G$,where $P$ is pressure and $G$ is the universal gravitational constant; then the dimensional formulas for $x$ and $z$ respectively are (here,$G = \frac{Fr^2}{m_1 m_2}$,$P = \frac{\text{Thrust}}{\text{Area}}$).

Similar Questions

Why does the concept of dimension have basic importance?

$A$ modified gravitational potential is given by $V = -\frac{GM}{r} + \frac{A}{r^2}$. If the constant $A$ is expressed in terms of gravitational constant $G$, mass $M$, and velocity of light $c$, then from dimensional analysis, $A$ is:

$A$ force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t$. The factor which is dimensionless,if $\alpha$ and $\beta$ are constants,is:

If time $(t)$,velocity $(u)$,and angular momentum $(I)$ are taken as the fundamental units,then the dimension of mass $(m)$ in terms of $(t)$,$(u)$,and $(I)$ is:

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$,having a pressure difference $P$ across its ends,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module