Question

For the equation of force \(F = Aa^b d^c\), where \(F\) is the force, \(A\) is the area, \(v\) is the velocity and \(d\) is the density, the values of \(a, b\) and \(c\) are respectively:

• A. \(1,2,1\)
• B. \(2,1,1\)
• C. \(1,1,2\)
• D. \(0,1,1\)

Hint:

Always equate powers of \(M\), \(L\), and \(T\) separately while using dimensional analysis.

Answer 1

The Correct Option is A

Step 1: Dimensional formula: \[ [F] = ML T^{-2} \]
Step 2: \[ [A] = L^2,\quad [v] = LT^{-1},\quad [d] = ML^{-3} \]
Step 3: \[ [A^a v^b d^c] = L^{2a}(LT^{-1})^b(ML^{-3})^c \] Equating dimensions: \[ M^c L^{2a+b-3c} T^{-b} = ML T^{-2} \] Solving: \[ a=1,\; b=2,\; c=1 \]