A spherical ball falls through viscous medium with terminal velocity `v`. If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be (neglect the effect of buoyancy.)

Options

A. `v`
B. `2v`
C. `4v`
D. `8v`

Answer

B

Explanation

`m=4/3pir^(3)rhom`
Keeping `m` constant if `r` is halved `rho` will increased by a factor of `8`.
Now, `v_(0)propr^(2)rho`
`v_(0)^(')prop(r^(2))/4(8rho)` or `v_(0)^(')prop2r^(2)rho`
Dividing `(v_(0)^('))/(v_(0)^('))=2` or `v_(0)^(')=2v_(0)`
or `v_(0)^(')=2v`