JEE MAIN - Physics (2024 - 31st January Evening Shift - No. 2)
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
$$L^{-2} M^1 T^0$$
$$L^2 M^{-1} T^1$$
$$L^0 M^{-1} T^1$$
$$L^{-2} M^{-1} T^1$$
Explanation
$$\begin{aligned}
& {[\mathrm{B}]=\mathrm{L}^2} \\
& \mathrm{~A}=\frac{\mathrm{x}^2}{\mathrm{tE}}=\frac{\mathrm{L}^2}{\mathrm{TML}^2 \mathrm{~T}^{-2}}=\frac{1}{\mathrm{MT}^{-1}} \\
& {[\mathrm{~A}]=\mathrm{M}^{-1 \mathrm{~T}}} \\
& {[\mathrm{AB}]=\left[\mathrm{L}^2 \mathrm{M}^{-1} \mathrm{~T}^1\right]}
\end{aligned}$$
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