Two geometrically identical homogeneous balls are manufactured of different materials. Their densities ball-`1` and ball-`2` are `800 kg//m^(3)` and `200 kg//m^(3)` respectively. Both balls are dropped from very high tower. Assume that the air resistance is proportional to the square of velocity. Determine the ratio of the maximum velocities of the ball -`1` to ball-`2`.

Options

A. `2`
B. `3`
C. `4`
D. `6`

Explanation

The ball will achieve its velocity when its acceleration is zero. So,
`m_(1)g=bv_(1_(max))^(2)`
`m_(2)g=bv_(2_(max))^(2)`
`((v_(1_(max)))/(v_(2_(max))))^(2)=(m_(1))/(m_(2))=(rho_(1))/(rho_(2))=4rArr(v_(1_(max)))/(v_(2_(max)))=2`