JEE PYQ: Units And Dimensions Question 16
Question 16 - 2019 (08 Apr Shift 2)
If Surface tension (S), Moment of Inertia (I) and Planck’s constant (h), were to be taken as the fundamental units, then dimensional formula for linear momentum would be:
(1) $S^{1/2} I^{3/2} h^{-1}$
(2) $S^{1/2} I^{1/2} h^{-1}$
(3) $S^{1/2} I^{1/2} h^0$
(4) $S^{3/2} I^{1/2} h^0$
Show Answer
Answer: (3)
Solution
$P = K S^a I^b h^c$. Comparing dimensions: $a+b+c=1$, $2b+2c=1$, $-2a-c=-1$. Solving: $a=1/2, b=1/2, c=0$. So $P = S^{1/2}I^{1/2}h^0$.
BETA
