Question

Pressure $P_r=\frac{3F{v}^2}{{\pi }^2{t}^{2}x}$ (where $P_r$ = Pressure F = force, v = velocity, t = time, x = distance)

State whether true or false: the above equation is dimentionally correct

• A. True
• B. False

Answer 1

The correct option is B False

Pressure $P_r=\frac{3F{v}^2}{{\pi }^2{t}^{2}x}$ (where $P_r$ = Pressure F = force, v = velocity, t = time, x = distance)

Dimension of L.H.S = $\left[P_r\right]=M^1{L}^{-1}{T}^{-2}$

Dimension of R.H.S. = $\frac{\left[3\right]\left[F\right]\left[V^2\right]}{\left[\pi \right]\left[t^2\right]\left[x\right]}=\frac{\left[M^1{L}^1{T}^{-2}\right]\left[L^2{T}^2\right]}{\left[T^2\right]\left[L\right]}=M^1{L}^2{T}^{-6}$

Dimension of L.H.S. and R.H.S are not same So the relation cannot be correct Sometimes a question is asked which is beyond our syllabus, then certainly it must be the question of dimensional analyses