Mechanical Properties of Fluids

Step 1: Find the pressure inside the larger bubble.
\(P_l=P_{atm}+\frac{4s}{3r}\)

Step 2: Find the pressure inside the smaller bubble.
\(P_s=P_l+\frac{4s}{r}\\~~~~=P_{atm}+\frac{4s}{3r}++\frac{4s}{r}\\~~~~=P_{atm}+\frac{16s}{3r}\)
Therefore, the excess pressure within  a smaller bubble, relative to the atmospheric pressure is \(\frac{16S}{3r}.\)
Hence, option (4) is the correct answer.