A mercury drop of radius R splits up into 1000 droplets of equal radii . The change in the surface area is

Options

A. `8piR^(2)`
B. `36piR^(2)`
C. `12piR^(2)`
D. `40piR^(2)`

Answer

B

Explanation

Volume of one drop = Volume of 1000 droplets
` :. 4/3 piR^(3) =100 (4/3 pir^(3))`
` :. R^(3) =1000r^(3) " " :. R = R/10`
` :.` Change in surface area
` = 1000 .4pir^(2) -4piR^(2)`
` = 4pi [ 1000 xx (R^(2))/100 -R^(2)] `
` :. dA = 4pi [10R^(2)-R^(2)]=36piR^(2)`