Question

Force is given by the expression, $F=A\cos \left(Bx\right)+C\cos \left(Dt\right)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is same as that of

• A. Velocity
• B. Velocity gradient
• C. Angular velocity
• D. Angular momentum

Answer 1

Answer: (A)

Velocity

Dimension of $D$ is $\left[T^{-1}\right]$.
Similarly, dimension of $B$ is $\left[L^{-1}\right]$.
Thus dimension of $\frac{D}{B}=\frac{\left[T^{-1}\right]}{\left[L^{-1}\right]}=\left[M^0{L}^1{T}^{-1}\right]$
So, the quantity $\frac{D}{B}$ represents velocity