Boyle's Law

Boyle's law, described in NCERT Class 11, Chapter 13 (Kinetic Theory), states that for a fixed mass of gas held at constant temperature the pressure and volume are inversely related, expressed as $P_1{V}_1=P_2{V}_2$. As the bubble rises through the water the surrounding pressure drops from 4 atm to 1 atm while the temperature stays constant, so we can equate the products directly. Substituting the values gives $4\times 2=1\times V_2$, hence $V_2=8$ cm cubed, meaning the bubble expands to four times its original size. The option 0.5 cm cubed applies the proportionality backwards, as though pressure and volume increased together. The option 2 cm cubed wrongly assumes volume is unaffected by pressure change. The option 4 cm cubed underestimates the expansion by using a factor of 2 rather than the true pressure ratio of 4. A magnitude check supports the result: since pressure fell to one quarter, volume must rise by the same factor, and $2\times 4=8$ cm cubed confirms both the direction and size of the change.