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CISCEISC (Science) ISC Class 11
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Terminal Velocity

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Terminal Velocity

  • Terminal velocity is the maximum velocity of a body moving through a viscous fluid.

  • It is attained when the force of resistance of the medium is equal and opposite to the force of gravity.

  • As the velocity is increasing the retarding force will also increase and a stage will come when the force of gravity becomes equal to the resistance force.

  • After that point velocity won’t increase and this velocity is known as terminal velocity.

  • It is denoted by ‘vt’.Wheret=terminal.

  • Mathematically:-

  • Terminal velocity is attained when the Force of resistance = force due to gravitational attraction.

`6pieta"rv"="mg"`

`6pieta"rv"="density"xx"V"_ g "(Because density"="m"/"V")`, density = `rho-sigma` where `rho` and `sigma` are the densities of the sphere and the viscous medium.

`6pieta"rv" = (rho-sigma)xx4/3pir^3g` where volume of the sphere(V)=`4/3pir^3`

By simplifying

`=(rho-sigma)"g"xx4/3r^2xx1/(6eta)`

`v_t=(2r^2(rho-sigma)g)/(9eta)`This is the terminal velocity. Where`(v=v_t)`

Problem: The terminal velocity of a copper ball of radius 2.0 mm falling through a tank of oil at 20oC is 6.5 cm s-1.Compute the viscosity of the oil at 20oC.Density of oil is 1.5 × 103 kg m-3, density of copper is 8.9 × 103 kg m-3.

Solution:

Given:`"V"_t=6.5xx10^-2ms^-1, a=2xx10^-3m,g=9.8  ms^-2, rho=8.9xx10^3kgm^-3, sigma=1.5xx10^3kgm^-3.`

From equation:` -v_t=(2r^2(rho-sigma)g)/(9eta)`

`=2/9((2xx10^-3m^2xx9.8ms^-2)/(6.5xx10^-2ms^-1))xx7.4xx10^3"kgm"^-3`

`=9.9xx10^-1"kgm"^-1"s"^-1`

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Related QuestionsVIEW ALL [21]

Two spheres of equal masses but radii r1 and r2 are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities are ____________.

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be ______.

Two solid spherical balls of radius r1 and r2 (r2 < r1), of density σ are tied up with a long string and released in a viscous liquid column of lesser density ρ and coefficient of viscosity η, with the string just taut as shown. The terminal velocity of spheres is ______.

Two drops of equal size are falling vertically through the air with a constant terminal velocity of 0.15 cm/s. What should be the velocity, if these drops coalesce to form one drop? 

A spherical ball of iron of radius 2 mm is falling through a column of glycerine. If densities of glycerine and iron are respectively 1.3 × 103 kg/m3 and 8 × 103 kg/m3. η for glycerine = 0.83 Nm-2 sec, then the terminal velocity is ______.

A piece of wood is taken deep inside a long column of water and released. It will move up

The radii of the two spheres P and Q of same material falling in the viscous liquid are in the ratio 3 : 2, their terminal velocities (P to Q) are in the ratio ______.

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