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A lead shot of $1 \,mm$ diameter falls through a long column of glycerine. The variation of the velocity with distance covered (s) is correctly represented by
A lead shot of $1 \,mm$ diameter falls through a long column of glycerine. The variation of the velocity with distance covered (s) is correctly represented by
Updated On: Apr 26, 2024
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The Correct Option is A
Solution and Explanation
In the beginning due to gravity pull, the lead shot will be accelerated and hence will move, with increasing velocity for some time When the viscous force balance the gravity pull, then the shot will move with constant velocity. As in the beginning, the velocity of shot is not fully linear with the effective distance covered by the shot.
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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.
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