A vector field v is expressed in spherical coordinates as:  v (r,θ,φ) = 2r cos θ er − r sin θ eθ Calculate ∇ × v and hence show that v is everywhere conservative.

Q: A convex lens has a focal length of 6 cm. A candle with a height of 7 cm is 17 cm away from the…

A: Using the thin lens formula, we can find the distance of the image from the lens: 1/f=1/do+1/di…

Q: Q2 Calculate the frequency of a wave with a wavelength of 3 cm. In which region that this frequency…

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Q: The drum has a weight of 60 lb and a radius of gyration of ko = 0.5 ft about its center of mass O.…

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Q: An electron moves with a speed of 7 x 106 m/s along the +x-axis. It enters a region where there is a…

A: The question deals with the calculation of the magnetic force acting on an electron as it moves…

Q: If you start at the equator and travel to 10 degrees north approx. how many kilometers (or miles)…

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Q: Turbulent flow has which of the following properties: O A. Associated with a very high Reynolds…

A: Turbulent flow Its a type of fluid (gas or liquid) flow in which the fluid undergoes irregular…

Q: A pulley of moment of inertia 2.0kg−m^2 is mounted on a wall as shown in the following figure. Light…

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Q: What hanging mass will stretch a 2.0m long, 0.50mm diameter steel wire by 1.0mm? Ysteel=20 *10^10…

A: Length of wire, L = 2.0 m Diameter of wire, d = 0.50 mm = 0.50 x 10-3 m Ysteel=20 x 1010 N/m2 Change…

Q: You are designing a highway which will be safe even if there is no friction between the tires of the…

A: The ideal embankmenr angle is given in radians by the formula, tan(θ)=V2rg where, θ= embankment…

Q: A diverging lens has a focal length of 19.8 cm. An object with a height of 7.7 cm is placed 28.5 cm…

A: Focal length ,f = -19.8 cm  (Focal length of diverging lens is negative) Object distance, u = -28.5…

Q: Michelson's interferometer played an important role in improving our understanding of light, and it…

A: Wavelength of laser lightλ=641.0nm =641.0x10-9m Distance moved from the mirror1 is (d) =1.720mm…

Q: A 12 kg is object is lifted by a rope from the first floor to the second floor, about 3.0 m. How…

A: Solution: Given: m = mass of object = 12 kg h = vertical height through which object is lifted = 3.0…

Q: The angular speed of an automobile engine is increased at a constant rate from 1310 rev/min to 3310…

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Q: In the attached figure, the RC circuit has been connected to the battery (E=Vo = 12 V) for a long…

A: Given Data: Potential (Vo) = 12 V.Resistance (R) = 35 kΩ = 35×103 Ω.Capacitance (C) = 12 mF =…

Q: 1a. This resistor has a resistance of 4800, and 32mA of current flows to the left into it. The right…

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Q: The current in a 70.0-mH inductor changes with time as I = 3.00t2 − 8.00t, where I is in amperes and…

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Q: A total charge of 72.0 nC is uniformly distributed on a conducting sphere with a radius of 5.00 cm.…

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Q: A convex lens has a focal length of 4 cm. A candle with a height of 8 cm is 10 cm away from the…

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Q: When kicking a football, the kicker rotates his leg about the hip joint.   a) If the velocity of…

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Q: Find the torque about the origin when a force of 31 N acts on the particle whose position vector is…

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Q: What is the probability that the n=1 electron of a hydrogen atom is found between r=0 and r=∞?…

A: The probability of finding the electron of a hydrogen atom between r=0 and r=∞ is equal to the total…

Q: Two teachers enter the teacher’s lounge which is kept at a constant temperature of 70 degrees…

A: Given Data: Temperature of the lounge = 70o C.Temperature of the coffee (T1(0)) = 220o C. To…

Q: The nonreflective coating on a camera lens with an index of refraction of 1.31 is designed to…

A: Solution: Given: n1 = refractive index of air = 1.00 n2 = refractive index of thin film coating =…

Q: A convex mirror has a focal length of -6 cm. A candle with a height of 7 cm is 30 cm away from the…

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Q: Olympian figure skaters are able to spin at about 4.9 revolutions/s. a) What is the magnitude of…

A: The rate of revolution of the skaters is 4.9 rev/s. The distance of the skater's nose from the axis…

Q: The Figure shows the result of a collision of a 10.00 kg ball with an object located at the origin.…

A: From the figure, we can see that the 10.00 kg ball collides with an object of unknown mass located…

Q: Current Attempt in Progress A concave mirror has a focal length of 36.0 cm. The distance between an…

A: See beloe

Q: Find the moment of inertia of the rod of mass m about the axis shown below by direct integration.…

A: To calculate the moment of inertia of a thin rod of mass M and length L about an axis through the…

Q: In the figure an electric field is directed out of the page within a circular region of radius R =…

A: The radius of the circular region, R=3.50cm×1m100cm=0.035m The magnitude of the electric field,…

Q: The primary mirror on a telescope is able to resolve objects that are theta o apart. If you replace…

A: The angular resolution of a telescope is determined by the diameter of its primary mirror or lens,…

Q: You decide to make another capacitor starting with two parallel conducting plates, of area A. Then…

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Q: A box is pulled with a force of 75 N at an angle of 45 degrees for a total distance of 15 m... a)…

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Q: An object is used to create an object the image distance is -104 cm the magnification is .9 and the…

A: We can use the thin lens equation to relate the object distance (u), image distance (v), and focal…

Q: A lens made out of a material with an index of refraction of 1.25 is a converging lens in air. Will…

A: Refractive index of lens, n =1.25  refractive index of water, n' = 1.33

Q: What makes fibre optics superior than copper wires in this context?

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Q: Which of the following would most likely be an insulator? a) a copper pipe b) a wooden spoon…

A: To chose most appropriate example of insulator provide in the above question.

Q: 1) A 2μC point charge is located at A(4, 3, 5) in free space. Find the electric field intensity…

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Q: Some unpolarized light has an intensity of 1325 W/m2 before passing through three polarizing…

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Q: A 20 µF capacitor is connected to a 60 V battery until it becomes fully charged.  The capacitor is…

A: Capacitance C = 20 micro farad Potential difference V = 60 volts

Q: Problem 4: Using the graph of a sin waves below estimate the phase difference A between the waves.…

A: The phase difference, ∆ϕ, can be found using the following relation. ∆tT=∆ϕ2π Where T is the period…

Q: A 2.15 kg block of iron at 415 °C is put in 0.625 kg of water at 15.0 °C. They come to equilibrium…

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Q: What are advantages of supercapacitor compared to batteries, fuel cells and conventional capacitors?

A: Super capacitors are a special types of capacitor that are manufactured for special purpose use.…

Q: Miniature black holes. Left over from the big-bang beginning of the universe, tiny black holes might…

A: Mass of black hole ( M ) = 3 ×1011 kg Acceleration due to gravity ( g ) = 9.83 m/s2 Mass of body ( m…

Q: Calculate the magnitude of the magnetic field at a point 13.0 cm from a long, thin conductor…

A: Current in the wire is I = 1.25 A

Q: A charge of +300 nC at a particular location experiences an electrostatic force of 0.2 N due to a…

A: Charge = q = 300 nC  Electrostatic force = F = 0.2 Newton.

Q: A mixture of red light (Avacuum = 640 nm) and green light (Avacuum = 512 nm) shines perpendicularly…

A: The wavelength of the red light in vacuum is 640 nm. The wavelength of the green light in vacuum is…

Q: A magnetic field is oriented at an angle of 57 ∘ to the normal of a rectangular area 4.8 cm by 6.6…

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Q: string of mass 10.00g and length 1.03m suspends a 26.00kg from the ceiling of an elevator. Determine…

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Q: true or false  According to the Bohr Model, electrostatic force is the source of centripetal force…

A: Neil Bhor proposed a atomic model applicable to hydrogen atom and hydrogen like atoms. According to…

Q: The system is released from rest with the spring initially stretched 2.8 in. Calculate the velocity…

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