Force F and density d are related as F=(α/β+√d) then find the dimensions of α :

Question

Force F and density d are related as F=(α/β+√d) then find the dimensions of α : (A) [ M 1 / 2 L -1 / 2 T -2] (B) [ M 3 / 2 L 1 /2 T 2] (C) [ M 3 / 2 L -1 / 2 T -2] (D) [ M 2 L -1 / 2 T 2]

Tardigrade Admin · Accepted Answer

[α]=[ F ][√ d ] = MLT -2[ ML -3]1 / 2 = M 3 / 2 L -1 / 2 T -2

Q. Force $F$ and density $d$ are related as $F = \frac{α}{β + d}$ then find the dimensions of $α$ :

$[M^{1/2} L^{- 1/2} T^{- 2}]$

$[M^{3/2} L^{1/2 T^{2}}]$

$[M^{3/2} L^{- 1/2} T^{- 2}]$

$[M^{2} L^{- 1/2} T^{2}]$

$[α] = [F] [d]$
$= M L T^{- 2} [M L^{- 3}]^{1/2}$
$= M^{3/2} L^{- 1/2} T^{- 2}$

Q. Force F and density d are related as F=β+d​α​ then find the dimensions of α :

[M1/2L−1/2T−2]

[M3/2L1/2T2]

[M3/2L−1/2T−2]

[M2L−1/2T2]

[α]=[F][d​] =MLT−2[ML−3]1/2 =M3/2L−1/2T−2