Question

The excess pressure inside a spherical drop of water is four times that of another drop. Their respective mass ratio is

• A. \(1:16\)
• B. \(8:1\)
• C. \(1:4\)
• D. \(1:64\)

Hint:

Excess pressure is 2T/r, so radius is inversely proportional to it. Mass goes as radius cubed.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The excess pressure inside a drop is \(P=\dfrac{2T}{r}\), so \(r\propto\dfrac{1}{P}\) for the same liquid.

Step 2: Radius Ratio
\(P_1=4P_2\), so \(\dfrac{r_1}{r_2}=\dfrac{P_2}{P_1}=\dfrac{1}{4}\).

Step 3: Mass
Mass \(m=\dfrac{4}{3}\pi r^{3}\rho\), so \(m\propto r^{3}\).

Step 4: Mass Ratio
\(\dfrac{m_1}{m_2}=\left(\dfrac{1}{4}\right)^{3}=\dfrac{1}{64}\).

Final Answer:
The mass ratio is 1 to 64. \[ \boxed{\text{(D) }1:64} \]