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Electrostatics: Coulomb's Law

Q- Four equal charges of + 3.0 x 10-7 C are placed on the corners of one face of a cube of edge length 10.0 cm. A charge of -3.0 x 10-7 C is placed at the center of the cube. What are the magnitude and the direction of the force on the charge at the center of the cube?

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Mechanics: Center of Mass and Momentum

Q- Two masses 5 kg and 15 kg are moving along x direction with velocities of 10 m/s and 2 m/s respectively. At an instant they are at positions 10 m and 70 m respectively

(A) Find position of their center of mass at this instant.

(B)  If the two will collide inelastically what is their common velo…

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Fluids: Floating

(On request: Fiaza Ali)

Q- A spherical brass shell of mass 2.50 kg barely floats in water such that it is completely submerged with the waterline just at its top. The inside of the shell is completely evacuated. The density of brass is 8600 kg/m3 and that of water is 1000 kg/m3.

(a) calculate the …

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Variable Mass: Conservation of Momentum

Q- A mass in the form of a solid cylinder, of radius R acted upon by no forces, moves parallel to its axis through a uniform cloud of fine dust, of volume density ρ, which is at rest. If the particles of dust which meet the mass adhere to it, and if M and u be the mass and the velocity at the begi…

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Current Electricity: Mesh Rule

Q- Write the mesh equations for the network and solve for the loop currents.

Solution:

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Mechanics: Translation and Rotation

Q- Block A of mass m = 10 kg is pulled from rest, on a horizontal surface by a massless rope passing over a pulley of same mass m = 10 kg, radius R = 0.25 m and moment of inertia I = 1.2 kg m2, rotates freely about its axis. The force applied at the end of the rope is P = 750 N. If the coefficient…

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Magnetic Circuit

Q- Find the current necessary to stablish a flux of ø = 3*10-4 Wb in the series magnetic circuit (shown in figure) consist of two parts of cast iron and steel cores. Length of each core is l = 0.3 m and the area of cross-section is A = 5*10-4 m2. Relative permittivity of cast iron is 5000 and that …

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Vectors: Force

Q- To pull a car, one end of a rope 25 m long is attached to the car. The other end is fastened to a tree. A man exerts a force of 500 N at the midpoint of the rope pulling it 1 meter to the side. What is the force exerted on the car in this position?

Solution:

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Sound Waves: Beats

Q- A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork. She can match the frequency of the tuning for by pulling out to increase length of her flute slightly. What was her initial frequency?

Solution:

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Heat: Gas Laws

Q- A diver releases an air bubble of volume 2.0 cm3 from a depth of 15 m below the surface of a lake where the temperature is 7.00C. What is the volume of the bubble when it reaches just below the surface of the lake where the temperature is 200C?

Solution:

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Ray Optics: Refraction

Q- The drawing shows a glass slab (n = 1.4) with a rectangular cross section. A ray of light strikes the slab at an incident angle of θ1 = 45°, enters the slab, and travels to point P. This slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total int…

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Electric Potential

Q- Ohmic heating raises the temperature of a tungsten filament to the point that electrons begin to "boil" off. A high voltage power supply establishes an accelerating potential difference of 900 V between the filament and a circular metal disk located 2.0cm away. The disk diameter is 1.0cm. Assumin…

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Newton's Laws Of Motion

Q- A body (weight 3000N) is supported by a bracket through a vertical cable. The bracket is composed of a horizontal bar and an inclined bar, both are rigidly fastened to the wall. Neglecting the weight of the bars and the cable, determine the magnitude of the reaction R1 exerted by the lower fixtur…

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Current Electricity: Superposition Method

Q- Using superposition, find the voltage Vacross the resistor R2.

Solution:

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Rotation: Rotor and Shaft

Q- A mirror is to be meant to oscillate at 10 cycles per minute and turns 30 degrees either side of the center line. The radius of the rotor is r and the length of the shaft L (considerably large). At what distance d from the center of the mirror the shaft is to be pinned and what is the distance of…

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Heat: Vapor pressure

Q- A room is filled with saturated moist air at 300C and a total pressure of 100 kPa. If the mass of dry air in the room is 100 kg, what is the mass of water vapor in the room?

Solution:

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Poynting Vector: E and B Fields In EM Waves

Q- A radio transmitter on the Earth’s surface radiates a sinusoidal wave with an average total power of 50 kW. Assuming that the transmitter radiates equally in all directions above the ground calculate the amplitudes Emax and Bmax detected by a satellite positioned 100 km from the transmitter.

S…

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Gravitation

Q- A 500 kg satellite circles the earth (5.97*1024 kg) along an orbit of radius 6.7*106m. Find

(a) The force attracting the satellite toward the earth.

(b) the satellite’s centripetal acceleration.

(c) The speed of the satellite along its orbit.

Solution:

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Center Of Mass

Q- Three particles, each with a mass of 0.25 kg, are located at ( - 4.0 m, 0), (2.0 m, 0), and (0, 3.0 m) and are acted on by forces F1 = 3 N along negative y-direction, F2 = 5 N along positive y-direction and F3 = 4 N along x direction  respectively. Find  position of center of mass of the system a…

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DC Circuit With Capacitor and Inductor

Q- The circuit has reached the steady state DC condition.

(a) Find the current through the voltage source

(b) Find the energy stored in the capacitor.

(c) find the energy stored in the inductor.

Solution:

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