Units And Dimensions Question 7
Question 7 - 2024 (31 Jan Shift 2)
Consider two physical quantities $\mathrm{A}$ and $\mathrm{B}$ related to each other as $\mathrm{E}=\frac{\mathrm{B}-\mathrm{x}^{2}}{\mathrm{At}}$ where $\mathrm{E}, \mathrm{x}$ and $\mathrm{t}$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
(1) $\mathrm{L}^{-2} \mathrm{M}^{1} \mathrm{~T}^{0}$
(2) $\mathrm{L}^{2} \mathrm{M}^{-1} \mathrm{~T}^{1}$
(3) $\mathrm{L}^{-2} \mathrm{M}^{-1} \mathrm{~T}^{1}$
(4) $\mathrm{L}^{0} \mathrm{M}^{-1} \mathrm{~T}^{1}$
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Answer: (2)
Solution:
$[\mathrm{B}]=\mathrm{L}^{2}$
$\mathrm{A}=\frac{\mathrm{x}^{2}}{\mathrm{tE}}=\frac{\mathrm{L}^{2}}{\mathrm{TML}^{2} \mathrm{~T}^{-2}}=\frac{1}{\mathrm{MT}^{-1}}$
$[\mathrm{A}]=\mathrm{M}^{-1} \mathrm{~T}$
$[A B]=\left[\mathrm{L}^{2} \mathrm{M}^{-1} \mathrm{~T}^{1}\right]$
