A uniform solid sphere of relative density 5 is released in water filled in a long vertical tube. Its terminal velocity achived is `V`. If another uniform solid sphere of same material but double the radius is released in the same water then the terminal velocity achived will be.

Options

A. `V`
B. `4V`
C. `(V)/(4)`
D. `2V`

Answer

B

Explanation

Initially the terminal velocity `V` of sphere of radius `a` is
`W_(eff)=6pietaaV` (1)`(W_(eff)=`weight`-`Buoyant force)
As the radius is doubled, mass is increased to 8 times and new terminal velocity will be
`8W_(eff)=6pieta2aV^(`)` .(2)
From (1) and (2) `V^(`)=4V`