Question

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

• A. $\left[M^{0} L T^{-1}\right] $
• B. $\left[M L^{2} T^{-3}\right] $
• C. $\left[M^{1} L^{1} T^{-2}\right]$
• D. $\left[M^{2} L^{2} T^{-3}\right]$

Answer 1

Answer: (B)

${[A]=\left[M L T^{-2}\right] }$
${[B]=\left[L^{-1}\right] }$
${[D]=\left[T^{-1}\right] }$
${\left[\frac{A D}{B}\right]=\frac{\left[M L T^{-2}\right]\left[T^{-1}\right]}{\left[L^{-1}\right]} }$
${\left[\frac{D}{B}\right]=\left[M L^{2} T^{-3}\right] }$