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
Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Which of the following is not a dimensionless quantity?
    View Solution
  • 2
    A torque meter is calibrated to reference standards of mass, length and time each with $5 \%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of$............\%$
    View Solution
  • 3
    Dimensional formula of heat energy is
    View Solution
  • 4
    The addition of three masses $1.6 \,g , 7.32 \,g$ and $4.238 \,g$, addressed upto proper decimal places is ....... $g$
    View Solution
  • 5
    If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ where  $\eta ,\rho $ and $r $ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of $x, y$ and $z$ are given by
    View Solution
  • 6
    Which of the following quantities is dimensionless
    View Solution
  • 7
     Match List $-I$ with List $-II$
      List $-I$   List $-II$
    $A$. Coefficient of Viscosity $I$. $[M L^2T^{–2}]$
    $B$. Surface Tension  $II$. $[M L^2T^{–1}]$
    $C$. Angular momentum $III$. $[M L^{-1}T^{–1}]$
    $D$. Rotational Kimeatic energy $IV$. $[M L^0T^{–2}]$
    View Solution
  • 8
    In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \mathrm{mm}$ and $(10 \pm 1) \mathrm{mm}$, respectively. In five successive measurements, the time period is found to be $0.52 \mathrm{~s}, 0.56 \mathrm{~s}, 0.57 \mathrm{~s}, 0.54 \mathrm{~s}$ and $0.59 \mathrm{~s}$. The least count of the watch used for the measurement of time period is $0.01 \mathrm{~s}$. Which of the following statement($s$) is(are) true?

    ($A$) The error in the measurement of $r$ is $10 \%$

    ($B$) The error in the measurement of $T$ is $3.57 \%$

    ($C$) The error in the measurement of $T$ is $2 \%$

    ($D$) The error in the determined value of $g$ is $11 \%$

    View Solution
  • 9
    A physcial quantity $x$ depends on quantities $y$ and $z$ as follows: $x = Ay + B\tan Cz$, where $A,\,B$ and $C$ are constants. Which of the following do not have the same dimensions
    View Solution
  • 10
    In a Vernier Calipers. $10$ divisions of Vernier scale is equal to the $9$ divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of $zero$ of the main scale and $4^{\text {th }}$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $1\,mm$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between $30$ and $31$ divisions of main scale reading and $6^{\text {th }}$ Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be $.......cm$
    View Solution