The dimensions of physical quantity X in the equation force =(X/√ text Density ) is given by :

Question

The dimensions of physical quantity X in the equation force =(X/√ text Density ) is given by : (A) M1 L4 T-2 (B) M2 L-2 T-1 (C) M1 / 2 L-1 / 2 T-2 (D) M1 L-2 T-1

Tardigrade Admin · Accepted Answer

beginaligned text [ mathrmX] &=[ mathrmF] ×[ρ]1 / 2 &=[ mathrmMLT-2] ×[( mathrmM/ mathrmL3)]1 / 2=[ mathrmM3 / 2 mathrm~L-1 / 2 mathrm~T-2] endaligned

Q. The dimensions of physical quantity $X$ in the equation force $= \frac{X}{Density}$ is given by :

$M^{1} L^{4} T^{- 2}$

$M^{2} L^{- 2} T^{- 1}$

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

$M^{1} L^{- 2} T^{- 1}$

$[X] = [F] \times [ρ]^{1/2} = [MLT^{- 2}] \times [\frac{M}{L ^{3}}]^{1/2} = [M^{3/2} L^{- 1/2} T^{- 2}]$

Q. The dimensions of physical quantity X in the equation force = Density ​X​ is given by :

M1L4T−2

M2L−2T−1

M1/2L−1/2T−2

M1L−2T−1