If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is :
Correct Option: , 3
(3) Energy, $E \propto A^{a} T^{b} P^{c}$
or, $\quad E=k A^{a} T^{b} P^{c}$ $\ldots$ (i)
where $k$ is a dimensionless constant and $a, b$ and $c$ are the exponents.
Dimension of momentum, $P=M^{1} L^{1} T^{-1}$
Dimension of area, $A=L^{2}$
Dimension of time, $T=T^{1}$
Putting these value in equation (i), we get
$M^{1} L^{2} T^{-2}=M^{c} L^{2 a+c} T^{b-c}$
by comparison
$c=1$
$2 a+c=2$
$b-c=-2$
$c=1, a=1 / 2, b=-1$
$\therefore E=A^{1 / 2} T^{-1} P^{\mathrm{l}}$
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