Home
Class 11
PHYSICS
A spherical solid ball of volume V is ma...

A spherical solid ball of volume V is made of a material of density `rho_(1)`. It is falling through a liquid of density `rho_(2) (rho_(2) lt rho_(1))`. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., `F_("viscous") = -kv^(2) (k gt 0)`. The terminal speed of the ball is

A

`(Vgrho_(1))/(k)`

B

`sqrt((Vgrho_(1))/(k))`

C

`(Vg(rho_(1)-rho_(2)))/(k)`

D

`sqrt(Vg(rho_(1) - rho_(2))/(k))`

Text Solution

Verified by Experts

The correct Answer is:
D
The forces acting on the ball are gravity force, buoyancy force and viscous force. When ball acquires terminal speed, it is in dynamic equilibrium, lt terminal speed of ball is `v_(T)`. So,

`Vrho_(2)g + kv_(T)^(2) = Vrho_(1)g, v_(T) = sqrt((V(rho_(1) - rho_(2))g)/(k))`
Promotional Banner

Topper's Solved these Questions

  • ELASTICITY AND VISCOCITY

    RESONANCE ENGLISH|Exercise Advanced Level Problems|9 Videos

  • ELASTICITY AND VISCOCITY

    RESONANCE ENGLISH|Exercise Exercise- 3 PART - I|7 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE ENGLISH|Exercise dpp 92 illustration|2 Videos

  • ELECTROMAGNETIC INDUCTION

    RESONANCE ENGLISH|Exercise Exercise|43 Videos

Similar Questions

Explore conceptually related problems

A spherical solild of volume V is made of a material of density rho_(1) . It is falling through a liquid of density rho_(2)(rho_(2) lt rho_(1)) . Assume that the liquid applies a viscous froce on the ball that is proportional ti the its speed v, i.e., F_(viscous)=-kv^(2)(kgt0) . The terminal speed of the ball is

A spherical solild of volume V is made of a material of density rho_(1) . It is falling through a liquid of density rho_(2)(rho_(2) lt rho_(1)) . Assume that the liquid applies a viscous froce on the ball that is proportional ti the its speed v, i.e., F_(viscous)=-kv^(2)(kgt0) . The terminal speed of the ball is

A solid ball of density rho_(1) and radius r falls vertically through a liquid of density rho_(2) . Assume that the viscous force acting on the ball is F = krv , where k is a constant and v its velocity. What is the terminal velocity of the ball ?

A ball of density rho is released from deep inside of a liquid of density 2 rho . It will move up

A body weighs W_(1) in a liquid of density rho_(1) and W_(2) in a liquid of density rho_(2) . What is the weight of body in a liquid of density rho_(3) ?

A ball of density rho is dropped from a height on the surface of a non-viscous liquid of density 2rho . Choose the correct options.

A ball of volume V and density rho_(1) is moved downwards by a distance 'd' in liquid of density rho_(2) . Find total change in potential energy of the system.

A solid sphere having volume V and density rho floats at the interface of two immiscible liquids of densites rho_(1) and rho_(2) respectively. If rho_(1) lt rho lt rho_(2) , then the ratio of volume of the parts of the sphere in upper and lower liquid is

A small ball of density rho_(0) is released from the surface of a liquid whose density varies with depth h as rho=(rho_(0))/2(alpha+betah) . Mass of the ball is m. Select the most appropriate one option.

A block of material has a density rho_(1) and floats three-fourth submerged in a liquid of unknown density. Show tht the density rho_(2) of the unknown liquid is given by rho_(2)=(4)/(3)rho_(1) .