Question

The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by relation of the type f = cm^xk^y, where c is a dimensionless constant. The values of x and y are –

• A. 1/2, ½
• B. – 1/2, – ½
• C. 1/2, – ½
• D. – 1/2, ½

Answer 1

Answer: (D)

– 1/2, ½

Answer 2

f = cm^x k^y

$\lbrack M^{0}L^{0}\text{T}\text{ }^{\text{-1}}\rbrack\ = \lbrack M^{1}\rbrack\text{x }\lbrack M^{0}L^{0}\text{T}\text{ }^{\text{-2}}\rbrack y\text{ }\text{M}^{0}L^{0}T^{\text{- 1}}\ = \text{ }\text{M}^{\text{x } + \text{ y}}\text{ }\text{L}^{0}\text{ }\text{T}^{\text{- 2y}}$

$\text{ x } + \text{ y } = \text{ 0}$ …(1)

$\text{ -2y } = \text{ -1}$ …(2)