Time period T,propto ,{P^a},{d^b},{E^c} | vedclass

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

Question

$T \alpha p^{a} d^{b} E^{c}$

$T=M^{0} L^{-1}$

$P=\left[M L^{-1} T^{-2}\right]$

$d=\left[M L^{-3}\right]$

$E=\left[M L^{2} T^{-2}\right]$

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

$T \alpha p^{a} d^{b} E^{c}$

$T=M^{0} L^{-1}$

$P=\left[M L^{-1} T^{-2}\right]$

$d=\left[M L^{-3}\right]$

$E=\left[M L^{2} T^{-2}\right]$

$M^{0} \cdot T^{\prime}=\left[M L^{-1} T\right]^{a}\left[M L^{-3}\right]^{b}\left[M L^{2} T^{-2}\right]^{c}$

$a+b+c=0-(1)$

$-a-3 b+2 c=0-(2)$

$-2 a-3 b-2 c=0-(3)$

Solve $e q^{n}(1),(2) \Delta(3)$

$a=\frac{-5}{6}, b=\frac{1}{2}, c=\frac{1}{3}$

Time period $T\,\propto \,{P^a}\,{d^b}\,{E^c}$ then value of $c$ is given $p$ is pressure, $d$ is density and $E$ is energy

Similar Questions

In equation $y=x^2 \cos ^2 2 \pi \frac{\beta \gamma}{\alpha}$, the units of $x, \alpha, \beta$ are $m , s ^{-1}$ and $\left( ms ^{-1}\right)^{-1}$ respectively. The units of $y$ and $\gamma$ are

Let us consider an equation

$\frac{1}{2} m v^{2}=m g h$

where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.

In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................

If velocity$(V)$, force$(F)$ and time$(T)$ are chosen as fundamental quantities then dimensions of energy are

If mass is written as $\mathrm{m}=\mathrm{kc}^{\mathrm{p}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $\mathrm{k}$ a dimensionless constant)