Question

In the following dimensionally consistent equation $F=\frac{X}{LinearDensity}+Y$, where F is the force, the dimensional formula for $X$ and $Y$ are given as:

• A. $M^2{L}^0{T}^{-2},{MLT}^{-2}$
• B. $M^2{L}^{-2}{T}^{-2},{MLT}^{-2}$
• C. ${MLT}^{-2},{ML}^2{T}^{-2}$
• D. $M^0{L}^0{T}^0,{ML}^0{T}^0$

Answer 1

The correct option is A $M^2{L}^0{T}^{-2},{MLT}^{-2}$

$F=\frac{X}{LinearDensity}$
$M^1{L}^1{T}^{-2}=\frac{X}{M^1{L}^{-1}}$
$X=M^2{T}^{-2}$
$Y=f=M^1{L}^1{T}^{-2}$
Hence, option A is correct.