Viscosity and Stoke's Law and Terminal PYQs: JEE Mains Physics

Showing 1–23 of 23 questions

1. 1. A small metallic sphere of diameter 2 mm and density \(10.5 g / cm ^3\) is dropped in glycerine having viscosity 10 Poise and density \(1.5 g / cm ^3\) respectively. The terminal velocity attained by the sphere is ___________ \(cm / s\).
   \(\left(\pi=\frac{22}{7}\right.\) and \(\left.g=10 m / s ^2\right)\) 2026 Hard
2. 2. A spherical body of radius \(r\) and density \(\sigma\) falls freely through a viscous liquid having density \(\rho\) and viscosity \(\eta\) and attains a terminal velocity \(v _0\). Estimated maximum error in the quantity \(\eta\) is : (Ignore errors associated with \(\sigma, \rho\) and g , gravitational acceleration) 2026 Hard
3. 3. A spherical liquid drop of radius \(R\) acquires the terminal velocity \(v_1\) when falls through a gas of viscosity \(\eta\). Now the drop is broken into \(64\) identical droplets and each droplet acquires terminal velocity \(v_2\) falling through the same gas. The ratio of terminal velocities \(v_1/v_2\) is ________. 2026 Medium
4. 4. Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of \(10 cm / s\) coalesce to form a bigger drop. The terminal velocity of bigger drop is _________ \(cm / s\). 2026 Hard
5. 5. The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is \(20 cm / s\). The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ \(cm / s\). 2026 Easy
6. 6. A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity) 2025 Medium
7. 7. A solid steel ball of diameter 3.6 mm acquired terminal velocity \(2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) while falling under gravity through an oil of density \(925 \mathrm{~kg} \mathrm{~m}^{-3}\). Take density of steel as \(7825 \mathrm{~kg} \mathrm{~m}^{-3}\) and g as 9.8 \(\mathrm{m} / \mathrm{s}^2\). The viscosity of the oil in SI unit is 2025 Medium
8. 8. In the experiment for measurement of viscosity ' \(\eta\) ' of given liquid with a ball having radius \(R\), consider following statements.
   A. Graph between terminal velocity V and R will be a parabola.
   B. The terminal velocities of different diameter balls are constant for a given liquid.
   C. Measurement of terminal velocity is dependent on the temperature.
   D. This experiment can be utilized to assess the density of a given liquid.
   E. If balls are dropped with some initial speed, the value of \(\eta\) will change.
   Choose the correct answer from the options given below: 2025 Hard
9. 9. A small spherical ball of radius \(r\), falling through a viscous medium of negligible density has terminal velocity ' \(v\) '. Another ball of the same mass but of radius \(2 r\), falling through the same viscous medium will have terminal velocity _______. 2024 Hard
10. 10. A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5\) \(\mathrm{kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately _______. (The coefficient of viscosity of water is \(9.8 \times 10^{-6}\) \(\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)\) 2024 Hard
11. 11. Mercury is filled in a tube of radius \(2 \mathrm{~cm}\) up to a height of \(30 \mathrm{~cm}\). The force exerted by mercury on the bottom of the tube is _______ \(\mathrm{N}\). (Given, atmospheric pressure \(=10^5 \mathrm{Nm}^{-2}\), density of mercury \(=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2\), \(\left.\pi=\frac{22}{7}\right)\) 2024 Hard
12. 12. Small water droplets of radius \(0.01 \mathrm{~mm}\) are formed in the upper atmosphere and falling with a terminal velocity of \(10 \mathrm{~cm} / \mathrm{s}\). Due to condensation, if \(8 \mathrm{such}\) droplets are coalesced and formed a larger drop, the new terminal velocity will be _______ \(\mathrm{cm} / \mathrm{s}\). 2024 Hard
13. 13. A Spherical ball of radius \(1 mm\) and density \(10.5 g / cc\) is dropped in glycerine of coefficient of viscosity \(9.8\) poise and density \(1.5 g / cc\). Viscous force on the ball when it attains constant velocity is \(3696 \times 10^{-x} N\). The value of \(x\) is \(\text { (Given, } g =9.8 m / s ^2 \text { and } \pi=\frac{22}{7} \text { ) }\) 2023 Medium
14. 14. An air bubble of diameter \(6\,mm\) rises steadily through a solution of density \(1750\,kg / m ^3\) at the rate of \(0.35\,cm / s\). The co-efficient of viscosity of the solution (neglect density of air) is \(..........\,Pas\) (given, \(g =10\,ms ^{-2}\)) 2023 Medium
15. 15. A small spherical ball of radius \(0.1 \,mm\) and density \(10^{4} \,kg m ^{-3}\) falls freely under gravity through a a distance \(h\) before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of \(h\) wil be \(m\). (Given \(g =10 \,ms ^{-2}\), viscosity of water \(=1.0 \times 10^{-5} \,N - sm ^{-2}\) ) 2022 Hard
16. 16. A water drop of radius \(1\,\mu m\) falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is \(1.8 \times 10^{-5}\,Nsm ^{-2}\) and its density is negligible as compared to that of water \(10^{6}\,gm ^{-3}\). Terminal velocity of the water drop is________ \(\times 10^{-6}\,ms ^{-1}\) (Take acceleration due to gravity \(=10\,ms ^{-2}\) ) 2022 Medium
17. 17. The diameter of an air bubble which was initially \(2\,mm\), rises steadily through a solution of density \(1750\,kg\,m\,m ^{-3}\) at the rate of \(0.35\,cms ^{-1}\). The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible). 2022 Medium
18. 18. The terminal velocity \(\left( v _{ t }\right)\) of the spherical rain drop depends on the radius ( \(r\) ) of the spherical rain drop as 2022 Easy
19. 19. A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ] 2021 Hard
20. 20. In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of \(h\) is proportional to : (ignore viscosity of air) 2020 Medium
21. 21. A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals 2019 Hard
22. 22. The average mass of rain drops is \(3.0\times10^{-5}\, kg\) and their avarage terminal velocity is \(9\, m/s\). Calculate the energy transferred by rain to each square metre of the surface at a place which receives \(100\, cm\) of rain in a year 2014 Medium
23. 23. In an experiment, a small steel ball falls through a Iiquid at a constant speed of \(10\, cm/s\). If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... \(cm/s\) 2013 Hard

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