If the dimensions of length are expressed as | vedclass

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

Question

(d) Length $\propto$ $G^{x}c^{y}h^{z}$

$L= {[{M^{ - 1}}{L^3}{T^{ - 2}}]^x}\,$${[L{T^{ - 1}}]^y}{[M{L^2}{T^{ - 1}}]^z}$

By comparing the power of

Vedclass · Accepted Answer

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

Vedclass · Answer

(d) Length $\propto$ $G^{x}c^{y}h^{z}$

$L= {[{M^{ - 1}}{L^3}{T^{ - 2}}]^x}\,$${[L{T^{ - 1}}]^y}{[M{L^2}{T^{ - 1}}]^z}$

By comparing the power of $M, L$ and $T$ in both sides we get $ - x + z = 0$, $3x + y + 2z = 1$ and $ - 2x - y - z = 0$

By solving above three equations we get

$x = \frac{1}{2},\,y = - \frac{3}{2},z = \frac{1}{2}$

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

The density of a material in $SI\, units$ is $128\, kg\, m^{-3}$. In certain units in which the unit of length is $25\, cm$ and the unit of mass $50\, g$, the numerical value of density of the material is

$M{L^{ - 1}}{T^{ - 2}}$ represents

If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are

Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is

$A$ and $B$ possess unequal dimensional formula then following operation is not possible in any case:-