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