Frequency is the function of density `rho`, length `lambda` and tension `T`. The period of oscillation is proporttional to

Options

A. `rho^(1//2) lambda^(2) T^(1//2)`
B. `rho^(3//2) lambda^(3//2) T^(-1//2)`
C. `rho^(1//2) lambda^(3//2) T^(-3//3)`
D. `rho^(1//2) lambda^(1//2) T^(3//2)`

Answer

A

Explanation

(1) Period of oscillation `t = (1)/(f r e q u e n c y f)`
`t prop rho^(a) lambda^(b) T^(c )`
`T prop [ML^(-3)] [L]^(b) [MLT^(-2)]^(c )`
`M^(0) L^(0), T^(1) prop M^(a + c) L^(-3a + b + c) T^(-2c)`
Comparing powers of `M, L` and `T`
`a + c = 0, - 3a + b c = 0, - 2c = 1`
`a = (1)/(2), b = 2, c = - (1)/(2)`
`t prop rho^(1//2) lambda^(2) T^(-1//2)`