Units And Dimensions Question 6
Question 6 - 2024 (31 Jan Shift 1)
A force is represented by $F=a ax^{2}+b t^{1 / 2}$
Where $x=$ distance and $t=$ time. The dimensions of $b^{2} / a$ are :
(1) $\left[ML^{3} T^{-3}\right]$
(2) $\left[MLT^{-2}\right]$
(3) $\left[ML^{-1} T^{-1}\right]$
(4) $\left[ML^{2} T^{-3}\right]$
Show Answer
Answer: (1)
Solution:
$F=ax^{2}+bt^{1 / 2}$
$[a]=\frac{[F]}{\left[x^{2}\right]}=\left[M^{1} L^{-1} T^{-2}\right]$
$[b]=\frac{[F]}{\left[t^{1 / 2}\right]}=\left[M^{1} L^{1} T^{-5 / 2}\right]$
$\left[\frac{b^{2}}{a}\right]=\frac{\left[M^{2} L^{2} T^{-5}\right]}{\left[M^{1} L^{-1} T^{-2}\right]}=\left[M^{1} L^{3} T^{-3}\right]$
