Consider a solid cylinder of height h, density `rho_s`, cross-sectional area A is floating in a liquid of density `rhol`. The frequency of vertical oscillations was found to be `g^(a) h^(b) rho_(i)^(c) , rho_(s)^d` when depressed slightly and released. Then what is the value of `(a^2b)/(cd)` ?

Answer

`0.5`

Explanation

Equation of motion,
`rho_sAh=(d^2x)/(dt^2)=-xrho_lAg`
`implies(d^2x)/(dt^2)=g/h(rho_t)/(rho_s)ximplies omega = sqrt((grho_1)/(hrho_s))`
`implies a =1/2 , b =(-1)/2, c =1/2,d =(-1)/2`
Now `(a^2b)/(cd)-((1/2)^2((-1)/2))/((1/2)((-1)/2))-1/2-0.5`