Question

The force F is given in terms of time t and displacement x by the equation F = A cosBx + C sin Dt. The dimensional formula of D/B is______

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

Answer 1

The correct option is D $\left[M^o{L}^1{T}^{-1}\right]$

$F=AcosBx+CsinDt$

the argument, $\theta$ of cos or sin should be dimensionless.
therefore,
dimension of Bx = $\left[MLT\right]$
$\left[B\right]\left[L^{\prime }\right]=\left[MLT\right]$

$\left[B\right]=\left[M{L}^{0}T\right]$

Similarly $\left[D\right]\left[T^{\prime }\right]=\left[MLT\right]$

$\left[D\right]=[ML{T}^0$
dimension of $DB=\frac{\left[ML{T}^0\right]}{\left[M{L}^{0}T\right]}$
= $\left[L^1{T}^{-1}\right]$