Two indetical spherical drops of water are falling (vertically downwards) through air with a steady velocity of `5(cm)/(sec)`. If both the drops coalesce (combine) to form a new spherical drop, the terminal velocity of the new drop will be (neglect buoyant force on the drops.)

Options

A. `5xx2(cm)/(sec)`
B. `5xxsqrt2(cm)/(sec)`
C. `5xx(4)^((1)/(3))(cm)/(sec)`
D. `(5)/(sqrt2)(cm)/(sec)`

Answer

C

Explanation

When two drops of radius `r` each combine to form a big drop, the radius of big drop will be given by
`(4)/(3)piR^3=(4pi)/(3)r^2+(4pi)/(3)r^3`
or `R^3=2r^2` or `R=2^((1)/(3))r`
Now `(V_R)/(V_r)=((R )/(R ))^2=2^((2)/(3))=4^((1)/(3))`
`V_R=5xx4^((1)/(3))(cm)/(s)`