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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_2ltrho_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(kgt0)`. The terminal speed of the ball is

A

`sqrt((V_(g) (p_(1)-p_(2)))/(k)`

B

`(Vgp_(1))/(k)`

C

`sqrt((Vgp_(1))/k)`

D

`(V_(g) (p_(1) gt p_(2)))/(k)`

Text Solution

Verified by Experts

The correct Answer is:
A
When ball attains terminal speed then buoyant force plux viscous force becomes equal to weight of ball.
`Vp_(2)g+kv^(2)=Vp_(1)g`
`rArr kv^(2)=V(p_(1)-p_(2))g`
`rArr v=sqrt((V(p_(1)-p_(2))g)/(k))`
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