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

Terms Bx and Dt are dimesionless being trigonometric functions.
For Bx to be dimensionless, x having dimension [L], B will require to have dimension $\left[L^{-1}\right]$
Similarly for Dt to be dimensionless, t having dimension [T], D will require to have dimension $\left[T^{-1}\right]$
So dimension of D/B is $\left[L{T}^{-1}\right]$