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1.Units, Dimensions and Measurement
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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
A
$ - \frac{5}{6}$
B
$\frac{1}{2}$
C
$\frac{1}{3}$
D
$1$
Solution
$T \alpha p^{a} d^{b} E^{c}$
$T=M^{0} L^{-1}$
$P=\left[M L^{-1} T^{-2}\right]$
$d=\left[M L^{-3}\right]$
$E=\left[M L^{2} T^{-2}\right]$
$M^{0} \cdot T^{\prime}=\left[M L^{-1} T\right]^{a}\left[M L^{-3}\right]^{b}\left[M L^{2} T^{-2}\right]^{c}$
$a+b+c=0-(1)$
$-a-3 b+2 c=0-(2)$
$-2 a-3 b-2 c=0-(3)$
Solve $e q^{n}(1),(2) \Delta(3)$
$a=\frac{-5}{6}, b=\frac{1}{2}, c=\frac{1}{3}$
Standard 11
Physics
