Q 11-01-020JEE MainEAMCET 1985 (Engineering)Easy
In the equation $F = A^a v^b d^c$, $F$ is force, $A$ is area, $v$ is velocity and $d$ is density. Dimensional analysis gives the exponents as
Answer: (A) $a=1,\ b=2,\ c=1$
Write the dimensions of each side:
$$[MLT^{-2}] = [L^2]^a\,[LT^{-1}]^b\,[ML^{-3}]^c = M^{c}\,L^{2a+b-3c}\,T^{-b}$$
Compare powers:
M: $c = 1$
T: $-b = -2 \Rightarrow b = 2$
L: $2a + b - 3c = 1 \Rightarrow 2a + 2 - 3 = 1 \Rightarrow a = 1$
So $F = A v^2 d$, the familiar form of the force of a fluid jet.
Solution by Sreeraj P, M.Sc Physics