Question

The force F is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt. The dimensional formula of $\frac{D}{B}$ is

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^0{L}^0{T}^{-1}\right]$
• C. $\left[M^0{L}^{-1}{T}^0\right]$
• D. $\left[M^0{L}^1{T}^{-1}\right]$

Answer 1

The correct option is D

$\left[M^0{L}^1{T}^{-1}\right]$

In the given equation 'Bx' and 'Dt' should be dimensionless.

$\Rightarrow X=\left[L\right]$ $\left[B\right]=\left[L^{-1}\right]$ and $\left[D\right]=\left[T^{-1}\right]$ then $\left[\frac{D}{B}\right]=\left[\frac{L}{T}\right]=\left[velocity\right]=\left[L{T}^{-1}\right]$