Units And Dimensions Question 5
Question 5 - 2024 (30 Jan Shift 2)
If mass is written as $\mathrm{m}=\mathrm{kc}^{\mathrm{P}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$ then the value of $\mathrm{P}$ will be : (Constants have their usual meaning with $\mathrm{k}$ a dimensionless constant)
(1) $1 / 2$
(2) $1 / 3$
(3) 2
(4) $-1 / 3$
Show Answer
Answer: (1)
Solution:
$\mathrm{m}=\mathrm{kc}^{\mathrm{P}} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}$
$\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{0}=\left[\mathrm{LT}^{-1}\right]^{\mathrm{P}}\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right]^{-1 / 2}\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]^{1 / 2}$
By comparing $\mathrm{P}=1 / 2$
