If the dimensions of length are expressed as | vedclass

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

Question

(D) Let the dimension of length be $L = G^x c^y h^z$.The dimensions are:$G = [M^{-1} L^3 T^{-2}]$$c = [L T^{-1}]$$h = [M L^2 T^{-1}]$Substituting thes

Vedclass · Accepted Answer

$(b)$ and $(c)$ both

Vedclass · Answer

(D) Let the dimension of length be $L = G^x c^y h^z$.The dimensions are:$G = [M^{-1} L^3 T^{-2}]$$c = [L T^{-1}]$$h = [M L^2 T^{-1}]$Substituting these into the equation:$[M^0 L^1 T^0] = [M^{-1} L^3 T^{-2}]^x [L T^{-1}]^y [M L^2 T^{-1}]^z$$[M^0 L^1 T^0] = M^{-x+z} L^{3x+y+2z} T^{-2x-y-z}$Comparing the powers on both sides:$1$) $-x + z = 0 \implies x = z$$2$) $3x + y + 2z = 1$$3$) $-2x - y - z = 0 \implies y = -2x - z$Substitute $x=z$ into $(3)$: $y = -2x - x = -3x$.Substitute $x=z$ and $y=-3x$ into $(2)$:$3x + (-3x) + 2x = 1$$2x = 1 \implies x = 1/2$.Since $x=z$,$z = 1/2$.Since $y = -3x$,$y = -3/2$.Thus,$x = 1/2, y = -3/2, z = 1/2$. Both options $(b)$ and $(c)$ are correct.

If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G, c$ and $h$ are the universal gravitational constant,speed of light,and Planck's constant respectively,then:

Similar Questions

Write and explain the principle of homogeneity. Check the dimensional consistency of the given equation: $x = x_{0} + v_{0}t + \frac{1}{2}at^{2}$.

$A$ 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:

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 dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$,its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,

Vedclass Test Series

Exam Paper Generator

Online Exam Module