Two rain drops of equal volume , falling with terminal velocity `10cms^(-1)` , merge while falling and forms a larger drop . Find the terminal velocity of the larger drop .

Explanation

Let the radius and volume of each drop be r and V respectively. When they merge and form a larger drop , its volume V. will be double the volume of each one of them. (As the mass and density remain constant.)
Let the radius of the bigger drop so formed be R.
Now `,V.=2V`
`therefore(4)/(3)piR^(3)=2((2)/(3)pir^(3))`
`thereforeR^(3)=2r^(3)`
`thereforeR=2^((1)/(3))r`
Let the terminal velocity of the smaller drop be v and that of the larger drop be v..
`thereforev=(2)/(9)(r^(2)g)/(eta)(rho-rho_(o))and`
`thereforev.=(2)/(9)(R^(2)g)/(eta)(rho-rho_(o))`
`therefore(v.)/(v)=(R^(2))/(r^(2))`
`thereforev.=(R^(2))/(r^(2))v=(2^((2)/(3)))xx10=15.87cms^(9-1)`