MHT CET · Physics · Mechanical Properties of Fluids
A metal sphere of radius 'R', density ' \(\varrho_{1}\) ' moves with terminal velocity ' \(\mathrm{v}_{1}\) ' through
a liquid of density ' \(\sigma^{\prime}\). Another sphere of same radius but of density ' \(\varrho_{2}\) ' moves
through same liquid. Its terminal velocity will be
- A \(\left[\frac{\varrho_{1}-\varrho_{2}}{\sigma}\right] \mathrm{v}_{1}\)
- B \(\left[\frac{\varrho_{2}+\sigma}{\varrho_{1}+\sigma}\right] \mathrm{v}_{1}\)
- C \(\left[\frac{\varrho_{1}+\varrho_{2}}{\sigma}\right] \mathrm{v}_{1}\)
- D \(\left[\frac{\mathrm{e}_{2}-\sigma}{\mathrm{e}_{1}-\sigma}\right] \mathrm{v}_{1}\)
Answer & Solution
Correct Answer
(D) \(\left[\frac{\mathrm{e}_{2}-\sigma}{\mathrm{e}_{1}-\sigma}\right] \mathrm{v}_{1}\)
Step-by-step Solution
Detailed explanation
\(6 \pi \eta R v_{1}=\frac{4}{3} \pi R^{3}(\rho_{1}-\sigma)\)
\(6 \pi \eta R v_{2}=\frac{4}{3} \pi R^{3}\left(\rho_{2}-\sigma\right)\)
\(\therefore \frac{v_{2}}{v_{1}}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma}\)
\(v_{2}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma} v_{1}\)
\(6 \pi \eta R v_{2}=\frac{4}{3} \pi R^{3}\left(\rho_{2}-\sigma\right)\)
\(\therefore \frac{v_{2}}{v_{1}}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma}\)
\(v_{2}=\frac{\rho_{2}-\sigma}{\rho_{1}-\sigma} v_{1}\)
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
- The pressure and density of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) changes adiabatically from \((\mathrm{P}, \rho)\) to \(\left(\mathrm{P}^{\prime}, \rho^{\prime}\right)\). If \(\frac{\rho^{\prime}}{\rho}=32\) then \(\frac{\mathrm{P}^{\prime}}{\mathrm{P}}\) should beMHT CET 2023 Hard
- The displacement of the particle executing linear S.H.M. is \(\mathrm{x}=0.25 \mathrm{sin}(11 \mathrm{t}+0.5) \mathrm{m}\). The period of S.H.M. is \(\left(\pi=\frac{22}{7}\right)\)MHT CET 2020 Easy
- A glass slab of thickness \(4 \mathrm{~cm}\) contains the same numbers of waves as \(5 \mathrm{~cm}\) of water when both are traversed by the same monochromatic ray of light. The refractive index of water is \(4 / 3\), what is that for glass?MHT CET 2011 Medium
- The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light (c) is (h \(=\) Planck's constant, \(\epsilon_{0}=\) permittivity of free space, \(\mathrm{e}=\) charge on electron \()\)MHT CET 2020 Medium
- A particle of mass 'm' moves along a circle of radius 'r' with constant tangential
acceleration. If kinetic energy 'E' of the particle becomes three times by the end of
third revolution after beginning of the motion then the magnitude of tangential
acceleration isMHT CET 2020 Easy - In Young's double slit experiment if the slit widths are in the ratio \(1: 9 .\) The ratio of the intensity at minima to that at maxima will beMHT CET 2011 Easy
More PYQs from MHT CET
- The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, areMHT CET 2023 Medium
- If the momentum of a body of mass ' \(m\) ' is increased by \(20 \%\) then its kinetic energy increases byMHT CET 2024 Hard
- An aircraft is moving with uniform velocity 150 m/s in the space. If all forces acting on it are balanced, then it willMHT CET 2019 Easy
- The element that does NOT form acidic oxide isMHT CET 2016 Medium
- \(\int_0^{\frac{\pi}{2}} \frac{\mathrm{~d} x}{1+(\cot x)^{101}}=\)MHT CET 2025 Easy
- In biogas plant, the role of acidogenic bacteria is toMHT CET 2018 Easy