Force F=(x/ρ )+y, where ρ is density then dimensional of x and y respectively are :

Question

Force F=(x/ρ )+y, where ρ is density then dimensional of x and y respectively are : (A) [M2 LT- 2],[M0 L 1 T0] (B) [M1 L1 T- 2],[M2 L2 T- 2] (C) [M2 L- 2 T- 2],[M1 L1 T- 2] (D) [M1 L2 T- 2],[M1 L1 T- 2]

Tardigrade Admin · Accepted Answer

From the principle of Homogeneity, [F]=[(x/ρ )]=[y]=MLT- 2[x]=[F][ρ ]=(M L T- 2)(M L- 3)=M2L- 2T- 2

Q. Force $F = \frac{x}{ρ} + y,$ where $ρ$ is density then dimensional of $x$ and $y$ respectively are :

$[M^{2} L T^{- 2}], [M^{0} L_^{1} T^{0}]$

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

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

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

From the principle of Homogeneity,
$[F] = [\frac{x}{ρ}] = [y] = M L T^{- 2} [x] = [F] [ρ] = (M L T^{- 2}) (M L^{- 3}) = M^{2} L^{- 2} T^{- 2}$

Q. Force F=ρx​+y, where ρ is density then dimensional of x and y respectively are :

[M2LT−2],[M0L_1T0]

[M1L1T−2],[M2L2T−2]

[M2L−2T−2],[M1L1T−2]

[M1L2T−2],[M1L1T−2]