Two soap bubbles in vacuum having radii 3 cm and 4 cm respectively coalesce under isothermal conditions to form a single bubble. What is the radius of the new bubble (in cm)?

Let r1 and r2 be the radii of two given soap bubbles and r be that of the coalesced bubble.Here, r1=30cm and r2=4cmSince a soap bubble has two free surfaces, total surface area of the coalesced bubble      =2×4πr2=8πr2Potential energy of the coalesced bubble, i.e.,       W=8πr2T                …(i)Similarly, if W1 and W2 are the potential energies of the two given bubbles,         W1=8πr12Tand  W2=8πr22T                 …(ii)Since the total energy of the system is conserved,              8πr2T=8πr12T+8πr22Tor    r2=r12+r22=(3)2+(4)2=25or    r=5cm