If the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is

  • A

    $T = k\sqrt {\rho {r^3}/S} $

  • B

    $T = k\sqrt {{\rho ^{1/2}}{r^3}/S} $

  • C

    $T = k\sqrt {\rho {r^3}/{S^{1/2}}} $

  • D

    None of these

Similar Questions

Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then

  • [IIT 1998]

Write and explain principle of homogeneity. Check dimensional consistency of given equation.

Write principle of Homogeneity of dimension.

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: [position $]=\left[X^\alpha\right] ;[$ speed $]=\left[X^\beta\right]$; [acceleration $]=\left[X^{ p }\right]$; [linear momentum $]=\left[X^{ q }\right]$; [force $]=\left[X^{ I }\right]$. Then -

$(A)$ $\alpha+p=2 \beta$

$(B)$ $p+q-r=\beta$

$(C)$ $p-q+r=\alpha$

$(D)$ $p+q+r=\beta$

  • [IIT 2020]

Number of particles is given by $n = - D\frac{{{n_2} - {n_1}}}{{{x_2} - {x_1}}}$ crossing a unit area perpendicular to $X-$axis in unit time, where ${n_1}$ and ${n_2}$ are number of particles per unit volume for the value of $x$ meant to ${x_2}$ and ${x_1}$. Find dimensions of $D$ called as diffusion constant