Consider two physical quantities A and B related to each other as where and have dimensions of energy, length and time respectively. The dimension of A B is

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Solution

Q.
Consider two physical quantities A and B related to each other as $E = \frac{B - x^{2}}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of A B is [2024]

1 $L^{- 2} M^{1} T^{0}$

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

3 $L^{- 2} M^{- 1} T^{1}$

4 $L^{0} M^{- 1} T^{1}$

Ans.
(2)

$[B] = L^{2}$

$A = \frac{x^{2}}{t E} = \frac{L^{2}}{T M L^{2} T^{- 2}} = \frac{1}{M T^{- 1}}$

$[A] = M^{- 1} T$

$[A B] = [L^{2} M^{- 1} T^{1}]$

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