Question:
The force is given in terms of time $t$ and displacement $x$ by the equation $F=A \cos B x+C \sin D t$
$\mathrm{F}=\mathrm{A} \cos \mathrm{Bx}+\mathrm{C} \sin \mathrm{Dt}$
The dimensional formula of $\frac{\mathrm{AD}}{\mathrm{B}}$ is :
Correct Option: , 2
Solution:
${[\mathrm{A}]=\left[\mathrm{MLT}^{-2}\right] }$
${[\mathrm{B}]=\left[\mathrm{L}^{-1}\right] }$
${[\mathrm{D}]=\left[\mathrm{T}^{-1}\right] }$
${\left[\frac{\mathrm{AD}}{\mathrm{B}}\right]=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{T}^{-1}\right]}{\left[\mathrm{L}^{-1}\right]} }$
${\left[\frac{\mathrm{AD}}{\mathrm{B}}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right] }$