MHT CET · Physics · Mechanical Properties of Fluids
Two small drops of mercury each of radius 'R' coalesce to form a large single drop.
The ratio of the total surface energies before and after the change is
- A \(\sqrt{2}: 1\)
- B \(2^{1 / 3}: 1\)
- C \(2: 1\)
- D \(2^{2 / 3}: 1\)
Answer & Solution
Correct Answer
(B) \(2^{1 / 3}: 1\)
Step-by-step Solution
Detailed explanation
\(\frac{4}{3} \pi R^{3} \times 2=\frac{4}{3} \pi R^{\prime 3}\)
\(R^{\prime}=2^{1 / 3} R\)
Total surface energy before \(=2 \times 4 \pi R^{2} T \quad(T=\) surface tension \()\)
Total surface energy after \(=4 \pi R^{\prime 2} T\)
\(\therefore \quad\) Ratio \(=\frac{2 \times R^{2}}{R^{\prime 2}}=\frac{2 \times R^{2}}{2^{2 / 3} R^{2}}=\frac{2}{2^{2 / 3}}=2^{1-\frac{2}{3}}=2^{1 / 3}\)
\(\therefore\) Ratio \(=2^{1 / 3}: 1\)
\(R^{\prime}=2^{1 / 3} R\)
Total surface energy before \(=2 \times 4 \pi R^{2} T \quad(T=\) surface tension \()\)
Total surface energy after \(=4 \pi R^{\prime 2} T\)
\(\therefore \quad\) Ratio \(=\frac{2 \times R^{2}}{R^{\prime 2}}=\frac{2 \times R^{2}}{2^{2 / 3} R^{2}}=\frac{2}{2^{2 / 3}}=2^{1-\frac{2}{3}}=2^{1 / 3}\)
\(\therefore\) Ratio \(=2^{1 / 3}: 1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- If the apertaure of a telescope is decreased the resolving power willMHT CET 2010 Medium
- Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What is the ratio of potential difference applied across them, so that the magnetic field at their centres is same?MHT CET 2022 Hard
- A thin uniform rod has mass 'M' and length 'L'. The moment of inertia about an axis perpendicular to it and passing through the point at a distance \(\frac{\mathrm{L}}{3}\) from one of its ends, will beMHT CET 2020 Easy
- An electron of mass ' \(m_e\) ' and a proton of mass ' \(m_p\) ' are kept in a uniform electric field. The ratio of the acceleration of electron \(\left(a_e\right)\) to the acceleration of proton \(\left(a_p\right)\) isMHT CET 2022 Easy
- What is the linear velocity if angular velocity \(\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}\) and radius \(\vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k})\) ?MHT CET 2025 Medium
- If fringe width is \(0.4 \mathrm{~mm}\), the distance between fifth bright and third dark band on same side isMHT CET 2009 Medium
More PYQs from MHT CET
- The point on the curve at which co-ordinate is changing times as fast as co-ordinate is ________MHT CET 2016 Medium
- In biprism experiment, if \(5^{\text {th }}\) bright band with wavelength \(\lambda_1^{\prime}\) coincides with \(6^{\text {th }}\) dark band with wavelength \(\lambda_2{ }^{\prime}\) then the ratio \(\left(\frac{\lambda_2}{\lambda_1}\right)\) isMHT CET 2023 Medium
- What is the relation between molality of the solution and molar mass of solute?MHT CET 2022 Easy
- Comparatively a large amount of pollen grains are wasted duringMHT CET 2025 Medium
- The equation of the circle whose centre lies on the line \(x-4 y=1\) and which passes through the points \((3,7)\) and \((5,5)\) isMHT CET 2022 Easy
- RNA shows the following characters EXCEPТ__________.MHT CET 2023 Easy