A small spherical ball falling through a viscuous medium of negligible density has terminal velocity v, Another ball of the same mass but of radius twice of the earlier falling through the same viscuous medium will have terminal velocity

Options

A. a)v
B. b)`v//4`
C. c)v//2`
D. d)2v

Answer

C

Explanation

Terminal velocity of the ball through a viscuous medium
`v=2/9 times g/(eta) (p- sigma)r^2`
or `v=2/9 times g/(eta) (p)r^2`
Because for viscuous medium of negligible density `(sigma=0)`
`therefore v=2/9 times g/(eta)times m/(4/3 pi r^3) times r^2[because p=m/(4/3pir^2)]`
or `v=2/9 times g/(eta)times m/(4/3pi r)`
`implies v prop 1/r`
For the second ball
`v. prop 1/(2r)`
`therefore v/v.=(2r)/r`
or `v.=v/2`