Two spherical soap bubbles of radii a and b in vacuum coalesce under isothermal conditions. The resulting bubble has a radius given by

Options

A. ` (( a + b )) / ( 2 )`
B. ` ( ab ) /( a + b ) `
C. ` sqrt ( a ^ 2 + b ^ 2 ) `
D. ` a + b `

Answer

C

Explanation

Since the bubbles coalesce in vaccum and there is no change in temperature, hence its surface energy does not change. This means that the surface area remains unchanged. Hence
` 4pi a ^ 2 + 4pi b ^ 2 = 4pi R^ 2 or R = sqrt ( a ^ 2 + b ^ 2 ) `