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The terminal speed of a sphere of gold (density = 19.5 g/cm3) is 0.2 m/s in a viscous liquid (density = 1.5 g/cm3). Find the terminal speed of a sphere of silver (density =10.5 g/cm3) of the same size in the same liquid (in m/s)
- a)0.2 m/s
- b)0.4 m/s
- c)0.133 m/s
- d)0.1m/s
Correct answer is option 'D'. Can you explain this answer?
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Terminal Velocity and Viscous Liquid
Terminal Velocity:
Terminal velocity is the maximum velocity that an object can attain when it is falling through a fluid. At terminal velocity, the gravitational force acting on the object is balanced by the viscous drag force of the fluid.
Viscous Liquid:
Viscosity is the measure of a fluid's resistance to flow. Liquids with high viscosity resist motion and have a thick, sticky consistency. Viscous liquids are commonly encountered in industrial and biological applications.
Solution:
Given, density of the sphere of gold=19.5 kg/m3, density of the liquid=1.5 kg/m3, and terminal speed=0.2 m/s.
We can use the following formula to calculate the terminal velocity of the sphere of gold in the given liquid:
v = (2mg/ρACd)1/2
where v is the terminal velocity, m is the mass of the sphere, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the sphere, Cd is the drag coefficient, which depends on the shape of the object.
We can simplify this equation by assuming that the sphere is a perfect sphere, and that the drag coefficient is 0.47 (which is the value for a smooth sphere). We can also assume that the cross-sectional area of the sphere is given by A = πr2, where r is the radius of the sphere.
Substituting the values given in the problem, we get:
v = (2 × 4/3πr3 × 9.8)/ (1.5 × πr2 × 0.47)
Simplifying this expression, we get:
v = 2r/3 × (19.6/7.05)1/2
v = 0.2r
Therefore, the terminal velocity of the sphere of gold in the given liquid is 0.2r.
Since the size of the sphere is the same in both cases, the correct answer is option D, 0.1 m/s.
Terminal Velocity:
Terminal velocity is the maximum velocity that an object can attain when it is falling through a fluid. At terminal velocity, the gravitational force acting on the object is balanced by the viscous drag force of the fluid.
Viscous Liquid:
Viscosity is the measure of a fluid's resistance to flow. Liquids with high viscosity resist motion and have a thick, sticky consistency. Viscous liquids are commonly encountered in industrial and biological applications.
Solution:
Given, density of the sphere of gold=19.5 kg/m3, density of the liquid=1.5 kg/m3, and terminal speed=0.2 m/s.
We can use the following formula to calculate the terminal velocity of the sphere of gold in the given liquid:
v = (2mg/ρACd)1/2
where v is the terminal velocity, m is the mass of the sphere, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the sphere, Cd is the drag coefficient, which depends on the shape of the object.
We can simplify this equation by assuming that the sphere is a perfect sphere, and that the drag coefficient is 0.47 (which is the value for a smooth sphere). We can also assume that the cross-sectional area of the sphere is given by A = πr2, where r is the radius of the sphere.
Substituting the values given in the problem, we get:
v = (2 × 4/3πr3 × 9.8)/ (1.5 × πr2 × 0.47)
Simplifying this expression, we get:
v = 2r/3 × (19.6/7.05)1/2
v = 0.2r
Therefore, the terminal velocity of the sphere of gold in the given liquid is 0.2r.
Since the size of the sphere is the same in both cases, the correct answer is option D, 0.1 m/s.
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The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer?.
The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The terminal speed of a sphere of gold (density =19.5 g/cm3)is0.2 m/sin a viscous liquid (density =1.5 g/cm3). Find the terminal speed of a sphere of silver (density=10.5 g/cm3)of the same size in the same liquid (inm/s)a)0.2 m/sb)0.4 m/sc)0.133 m/sd)0.1m/sCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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