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1.Units, Dimensions and Measurement
hard
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
A
$\mathrm{L}^{-2} \mathrm{M}^1 \mathrm{~T}^0$
B
$\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1$
C
$\mathrm{L}^{-2} \mathrm{M}^{-1} \mathrm{~T}^1$
D
$\mathrm{L}^0 \mathrm{M}^{-1} \mathrm{~T}^1$
(JEE MAIN-2024)
Solution
${[B]=L^2}$
$A=\frac{x^2}{t E}=\frac{L^2}{T^2 T^{-2}}=\frac{1}{M^{-1}}$
${[A]=M^{-1} T}$
${[A B]=\left[L^2 M^{-1} T^1\right]}$
Standard 11
Physics
