MHT CET · Physics · Mechanical Properties of Fluids
When a mercury drop of radius ' \(R\) ' splits up into 1000 droplets of radius ' \(r\) ', the change in surface energy is ( \(T=\) surface tension of mercury)
- A \(8 \pi \mathrm{R}^2 \mathrm{~T}\)
- B \(16 \pi \mathrm{R}^2 \mathrm{~T}\)
- C \(\quad 34 \pi \mathrm{R}^2 \mathrm{~T}\)
- D \(\quad 36 \pi R^2 T\)
Answer & Solution
Correct Answer
(D) \(\quad 36 \pi R^2 T\)
Step-by-step Solution
Detailed explanation
As volume remains constant,
\(\mathrm{R}^3=1000 \mathrm{r}^3\)
\(\therefore \quad \mathrm{n}^{\prime}=10 \mathrm{r}\) or \(\mathrm{r}=\frac{\mathrm{R}}{10}\)
Change in surface area
\(\begin{aligned}
& =\left(1000 \times 4 \pi r^2\right)-4 \pi R^2 \\
& =4 \pi\left(1000 \times \frac{R^2}{100}-R^2\right)=36 \pi R^2
\end{aligned}\)
Surface energy, \(T \Delta A=36 \pi R^2 T\)
\(\mathrm{R}^3=1000 \mathrm{r}^3\)
\(\therefore \quad \mathrm{n}^{\prime}=10 \mathrm{r}\) or \(\mathrm{r}=\frac{\mathrm{R}}{10}\)
Change in surface area
\(\begin{aligned}
& =\left(1000 \times 4 \pi r^2\right)-4 \pi R^2 \\
& =4 \pi\left(1000 \times \frac{R^2}{100}-R^2\right)=36 \pi R^2
\end{aligned}\)
Surface energy, \(T \Delta A=36 \pi R^2 T\)
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
- The displacement of a particle performing S.H.M is given by \(x=5 \sin (3 t+3)\), where \(x\) is in \(\mathrm{cm}\) and \(t\) is in second. The maximum acceleration of the particle will beMHT CET 2021 Easy
- A circular coil of radius ' \(r\) ' and number of turns ' \(n\) ' carries a current ' \(I\) '. The magnetic fields at a small distance ' \(h\) ' along the axis of the coil \(\left(B_a\right)\) and at the centre of the coil \(\left(\mathrm{B}_{\mathrm{c}}\right)\) are measured. The ralation between \(B_c\) and \(B_a\) isMHT CET 2023 Hard
- \(U\) is the PE of an oscillating particle and \(F\) is the force acting on it at a given instant. Which of the following is true ?MHT CET 2010 Medium
- Two vectors of same magnitude have a resultant equal to either of the two vectos. The angle between two vectors isMHT CET 2020 Easy
- Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is
\([\mu_0 \rightarrow \text {permeability of free space, } m \rightarrow\) \(\text {mass of electron} \ \varepsilon_0 \rightarrow \text {permittivity of free space, }\) \(h \rightarrow \text {Planck's constant}]\)MHT CET 2022 Hard - Advantage of optical fibre isMHT CET 2008 Easy
More PYQs from MHT CET
- Which of the following dissolves in ionic solvents?MHT CET 2012 Easy
- If \(y^{2}=a x^{2}+b x+c, \quad\) where \(\quad a, b, c\) are constants, then \(y^{3} \frac{d^{2} y}{d x^{2}}\) is equal toMHT CET 2007 Easy
- Select the INCORRECT statement with respect to heart sounds.MHT CET 2022 Easy
- Which from following polymers is a ureaformaldehyde resin?MHT CET 2024 Medium
- Which among the following is an example of branched chain polymer?MHT CET 2023 Easy
- \(\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}}(\sin x)^{-4} \mathrm{~d} x\) has the valueMHT CET 2024 Hard