Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1} = 8\pi_{2}\right)$ and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \,\rho_{2}$. The ratio of their terminal velocities would be :
- $\frac{79}{72}$
- $\frac{19}{36}$
- $\frac{39}{72}$
- $\frac{79}{36}$
The Correct Option is D
Solution and Explanation
$\frac{v_{1}}{v_{2}} = \left(\frac{r_{1}}{r_{2}}\right)^{2} \frac{\left(\sigma_{1} - \rho\right)}{\left(\sigma_{2} - \rho\right)}$
$= \left(\frac{1}{2}\right)^{2} \left(\frac{8\rho_{2} - 0.1 \rho_{2}}{\rho_{2} - 0.1 \rho_{2}}\right) = \frac{79}{36}$
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In an experiment to determine the figure of merit of a galvanometer by half deflection method, a student constructed the following circuit. He applied a resistance of \( 520 \, \Omega \) in \( R \). When \( K_1 \) is closed and \( K_2 \) is open, the deflection observed in the galvanometer is 20 div. When \( K_1 \) is also closed and a resistance of \( 90 \, \Omega \) is removed in \( S \), the deflection becomes 13 div. The resistance of galvanometer is nearly:
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Concepts Used:
Viscosity
Viscosity is a measure of a fluid’s resistance to flow. The SI unit of viscosity is poiseiulle (PI). Its other units are newton-second per square metre (N s m-2) or pascal-second (Pa s.) The dimensional formula of viscosity is [ML-1T-1].
Viscosity: Formula
Viscosity is measured in terms of a ratio of shearing stress to the velocity gradient in a fluid. If a sphere is dropped into a fluid, the viscosity can be determined using the following formula:
η = [2ga2(Δρ)] / 9v
Where ∆ρ is the density difference between fluid and sphere tested, a is the radius of the sphere, g is the acceleration due to gravity and v is the velocity of the sphere.
Viscosity: Types
- Dynamic viscosity: When the viscosity is measured directly by measuring force. It is defined as the ratio of shear stress to the shear strain of the motion. Dynamic viscosity is used to calculate the rate of flow in liquid.
- Kinematic viscosity: There is no force involved. It can be referred to as the ratio between the dynamic viscosity and density of the fluid. It can be computed by dividing the dynamic viscosity of the fluid with fluid mass density.
- Laminar flow: Laminar flow is the type of flow in which the fluid moves smoothly or in a regular path from one layer to the next. Laminar flow occurs in lower velocities.