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Refraction Through A Prism

Q- A horizontal beam of light that is incident on an equilateral prism. The base of the prism is horizontal. The prism (n = 1.40) is surrounded by a liquid whose index of refraction is 1.60. Determine the angle of emergence from the other surface, that is the exiting light makes with the normal to t…

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Sound and Vibration

Q- A heavy piece of hanging sculpture is suspended by a 90 cm long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?

Solution:

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Mechanics: Conservation of momentum

Q- Two railroad cars moving on same track towards each other. One of mass 10000 kg with speed 0.3 m/s and the other of mass 15000 kg with speed of 0.1 m/s.

(a) What is the magnitude of their common velocity after they coule together?

(b) How much kinetic energy is lost during collision?   

So…

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Thermodynamics: Specific Heat Capacity

Q- A well-sealed room contains 80 kg of air at 200 kPa and 25°C. Now solar energy enters the room from windows at an average rate of 1 kJ/s while a 100-W fan is turned on to circulate the air in the room. If heat transfer through the walls is negligible, what will be the air temperature in the room …

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Rotation: Toppling

Q- I have a 1.5 m tall air compressor that weights 50 kg with a 0.5 m square base. I have a cart that is 1m x 2m. The surface of the cart where the compressor will be mounted is 0.25 m off the ground. The cart wheels are in the corners, it is rated to carry 500 kg and weighs 75 kg. If the compressor…

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Electrostatics: Induced Charges

Q- A point charge q is placed between two infinitely large conducting parallel planes with distance d between them, such that it is at a distance x from one plane.  Find the charges induced on each plane.

Solution:

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Motion In A Plane

Q- A small ball is suspended from point A by a thread of length L.  A nail is driven into the wall at a distance of L/2 below A, at O.  The ball is drawn so that the thread takes up a horizontal position.

(a) At what point in the ball’s trajectory will the tension in the thread disappear?
(b)…

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Alternating Currents

Q - An AC generator supplies an rms voltage of 5.00 V to an RC circuit. At a frequency of 20.0 kHz the rms current in the circuit is 37.0 mA; at a frequency of 30.0 kHz the rms current is 50.0 mA. What are the values of R and C in this circuit?

Solution:

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kinematics

(Requested by Merjan)

Q – Two cars were moving on parallel lanes in one direction. One car had speed 60 km/hour, while the other had speed of 65 km/hr. At time 8:30 AM, the distance between the cars was 8 km. 

(a)  How far a way from each another the were at 9:20 AM that day?

(b)  At what ti…

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Ray Optics: Refraction

Q- Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors emerge from the glass at the same angle of refraction. The red light has an angle of incidence of 35.96°. What is the angle of incidence of the violet light? Give your answer to …

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Speed of Bullet

Q- A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown. Derive a formula for the bullet speed v in terms of D, T and a measured angle θ between the position of the hole in the first disk and that of the hole in the second.…

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Errors: Measuring Speed of Light

Q- Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the return light from his assistant’s lantern, which is opened when the assistant sees the light from Galileo’s lantern. What distance d must separate Galileo from his assist…

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Harmonic Oscillations

Q- A harmonic force F0 sin(ωt) is applied to mass m1 which in turn is coupled to springs of spring constants k1, k2 and k3. Let x1 and x2 ­be the deviations from equilibrium for m1 and m2, respectively.  The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for …

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Radioactivity

Q- Kr-85 is a radioactive isotope that is used in measuring paper thickness. It decays by emission with a half-life of 10.8 years

(a) Write down the decay equation showing the daughter isotope and decay products of this process.

(b) A Kr-85 source had activity 30 mCi when new. Estimate its activit…

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Gravitation: Force inversely proportional to cube of distance.

Q- Consider an object of mass m, moving in a circular orbit, subject to a central attractive for F whose magnitude is given by F(r) = h/r3.

(a)What are the dimensions of h?

(b) Show that the angular momentum for the motion is uniquely determined by h and m.

(c) What is the resulting relatio…

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Circuit Analysis

Q - For the multiple ladder configuration of Figure,

(a) Determine current I through battery

(b) Calculate current I4 through resistance R4

(c) Find current I6 through resistance R6

(d) Find current I10 through resistance R10

Solution:

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Momentum-Vector

Q- A 3.00 kg particle has a velocity of (3.00 i - 4.00 j) m/s.

(a) Find its x and y components of momentum.

(b) Find the magnitude and direction of its momentum

Solution:

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Electromagnetism: Moving Charge in a Magnetic Field

Q- In an experiment with cosmic rays, a vertical beam of particle that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field of 0.250 T and is bent in a semicircle of diameter 95.0 cm as shown in the diagram 

(a) Find the speed of the particles an…

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Force And Torque: Toppling

Q- A 2 m tall cylindrical compressor of mass 100 kg and 50 cm in diameter (base) is placed on a large cart. If there is sufficient friction to avoid any sliding, what is the maximum acceleration of the cart on level road for which the compressor will not topple.

Solution:

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Fiber Optics: Dual Core Cable

Q- The diagram shows the end of a fiber optic cable with core refractive index 1.5 and cladding refractive index 1.4

(a) Find the critical angle at which light in the core is just totally internally reflected at X.

(b) Find the angle of incidence at A for light which is just internally reflecte…

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