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

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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

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