In air, a charged soap bubble of radius R breaks into 64 small soap bubbles of equal radius r . The ratio of mechanical force per unit area of big soap bubble to that of a small bubble is

Step-by-step solution

When a soap bubble of radius R breaks into 64 small bubbles of equal radius r , the volume of soap solution remains constant. 4 3 R^3 = 64 4 3 r^3 Solving gives R^3 = 64r^3 and R = 4r . The mechanical force per unit area inside a soap bubble is the excess pressure due to surface tension, given by P = 4T radius . For the large bubble, P_ big = 4T R For a small bubble, P_ small = 4T r The ratio is P_ big P_ small = r R Substituting R = 4r gives P_ big P_ small = 1 4 . Since the problem specifies mechanical force per