MHT CET · Physics · Mechanical Properties of Fluids
A steel ball of radius 6 mm has a terminal speed of \(12 \mathrm{cms}^{-1}\) in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?
- A \(12 \mathrm{cms}^{-1}\)
- B \(9 \mathrm{cms}^{-1}\)
- C \(6 \mathrm{cms}^{-1}\)
- D \(3 \mathrm{cms}^{-1}\)
Answer & Solution
Correct Answer
(D) \(3 \mathrm{cms}^{-1}\)
Step-by-step Solution
Detailed explanation
Terminal speed,
\(v=\frac{2 r^2 g\left(\rho-\rho_L\right)}{9 \eta}\)
Since density of balls and liquid remains the same,
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}\right)^2=\left(\frac{6}{3}\right)^2=4 \\
& \therefore \quad \mathrm{v}_{\mathrm{B}}=\frac{\mathrm{v}_{\mathrm{A}}}{4}=\frac{12}{4}=3 \mathrm{cms}^{-1}
\end{aligned}\)
\(v=\frac{2 r^2 g\left(\rho-\rho_L\right)}{9 \eta}\)
Since density of balls and liquid remains the same,
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}\right)^2=\left(\frac{6}{3}\right)^2=4 \\
& \therefore \quad \mathrm{v}_{\mathrm{B}}=\frac{\mathrm{v}_{\mathrm{A}}}{4}=\frac{12}{4}=3 \mathrm{cms}^{-1}
\end{aligned}\)
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 output of a 'NAND' gate is shown in the truth-table (A and B are inputs, \(\mathrm{Y}\) is output)
MHT CET 2022 Easy - The Boolean equation for the circuit given in the figure is
MHT CET 2021 Easy - Electromagnetic waves of wavelength ranging from \(100 Å\) A to \(400 Å\) comes underMHT CET 2012 Easy
- A glass tube of \(1 \mathrm{~m}\) length is filled with water. The water can be drained out slowly from the bottom of the tube. If vibrating tuning fork of frequency \(500 \mathrm{~Hz}\) is brought at the upper end of the tube then total number of resonances obtained are [Velocity of sound in air is \(320 \mathrm{~ms}^{-1}\) ]MHT CET 2021 Hard
- A source and listener are both moving towards each other with speed \(\frac{\mathrm{V}}{10}\). (where V is speed of sound) If the frequency of sound note emitted by the source is ' \(n\) ', then the frequency heard by the listener would be nearlyMHT CET 2024 Easy
- An inductance coil has a resistance of \(100 \Omega\). When are a.c. signal of frequency \(100 \mathrm{Hzis}\) applied to the coil, the voltage leads the current by \(45^{\circ}\). The inductance of the coil in henry is \(\left[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right]\)MHT CET 2022 Easy
More PYQs from MHT CET
- What is the highest oxidation state exhibited by any transition element among all ?MHT CET 2020 Easy
- Select the INCORRECT pair with respect to mode of excretion.MHT CET 2022 Medium
- Neuroglia cells show following characters EXCEPTMHT CET 2020 Easy
- The equation of motion of a particle moving along a straight line is \(s=2 t^{3}-9 t^{2}+12 t\), where the units of \(s\) and \(t\) are centimetre and second. The acceleration of the particle will be zero afterMHT CET 2009 Easy
- Which of the following is Mendius reduction?MHT CET 2024 Easy
- Which of the following salts will not undergo hydrolysis?MHT CET 2011 Easy