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