Question

In the following equation x, t and F represent respectively displacement, time and force:

$F=a+bt+\frac{1}{c+dx}+Asin(\omega t+\varphi )$. The dimensional formula for 'Ad' is

• A. $T^{-1}$
• B. $L^{-1}$
• C. $M^{-1}$
• D. $T{L}^{-1}$

Answer 1

The correct option is B $L^{-1}$

$F=a+bt+\frac{1}{c+dx}+Asin(\omega t+\varphi )$

The dimensions of are same as that of force

$\therefore \left[A\right]=\left[F\right]=\left[ML{T}^{-2}\right]$

Also, the dimensions of $\frac{1}{c+dx}$ must be same as that of force

$\therefore \frac{1}{c+dx}=F\Rightarrow \left[\frac{1}{C}\right]=\left[F\right]$

$\therefore \left[c\right]=\left[M^{-1}{L}^{-1}{T}^2\right]$

Also, the dimension of is same as that of

$\therefore \left[d\right]=\frac{\left[c\right]}{\left[x\right]}=\left[M^{-1}{L}^{-2}{T}^2\right]$

$\therefore \left[Ad\right]=\left[ML{T}^{-2}\right]\left[M^{-1}{L}^{-2}{T}^2\right]=\left[L^{-1}\right]$