Question

If frequency can be represented as f = (radius)a (density)b (surface tension)c. Find a, b, c?

• A. a = \(\frac{3}{2}\), b = \(\frac{1}{2}\), c = \(\frac{-1}{2}\)
• B. a = \(\frac{-3}{2}\), b = \(\frac{-1}{2}\), c = \(\frac{1}{2}\)
• C. a = \(\frac{-3}{2}\), b = \(\frac{1}{2}\), c = \(\frac{-1}{2}\)
• D. a = \(\frac{1}{2}\), b = \(\frac{3}{2}\), c = \(\frac{-1}{2}\)

Answer 1

The Correct Option is B

M⁰L⁰T^–1 = L^a(ML^–3)^b(MT^–2)^c
M⁰L⁰T^–1 = L^aM^bL^–3b McT^–2c
Equivalent the power of MLT
M \(\Rightarrow\) 0 = b + c
L \(\Rightarrow\) 0 = a – 3b
T \(\Rightarrow\) –1 = – 2c
a = \(\frac{-3}{2}\), b = \(\frac{-1}{2}\), c = \(\frac{1}{2}\)