A spherical solid ball of volume V is made of a material of density p1 It is falling through a liquid of density `p_(2) (p_(2) lt p_(1))`. Assume the 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

Options

A. `dqrt((Vg(p_(1)-p_(2)))/k)`
B. `(Vgp_(1))/k`
C. `sqrt((Vgp_(1))/k)`
D. `(Vg(p_(1)gtp_(2)))/k`

Answer

A

Explanation

The condition for terminal speed `(v_(t))` is
Weight = Buoyant force + Viscous force
`thereforeVp_(1)g=Vp_(2)g+kv_(t)^(2)`
`thereforev_(t)=sqrt((V_(g)(p_(1)-p_(2)))/k)`
So Correct choice is (a).