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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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Standing Waves: Vibrating string

Q- Figure shows the standing wave on a string, oscillating at frequency fo.

(a) How many antinodes will there be if the frequency is doubled to 2fo.

(b) If the tension in the string is increased by a factor of four, for what frequency will the string continue to oscillate as a standing wave with…

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Current Electricity: Kirchhoff's laws

Q- Find the mesh currents and the voltage Vab for the given network. The source is the current source supplying a current of 3 A.

Solution:

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Kinematics: Projectile Motion

Q- A rocket is fired at an angle of 600 with horizontal and accelerates in a straight line at 25ms-2 for 2.5s before the rocket motor stops and it eventually falls to the ground. Neglecting air resistance

(a) Make a labelled sketch of the rockets trajectory starting from the launch point. Include …

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Ray Optics: Concave Mirror

Q- A 3.0-cm-tall domino is located 100 cm from a concave spherical mirror of R = 30 cm. Locate the position of the image and find its magnification.

Solution:

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Heat: Saturated Vapor Pressure

Q- A 1 m3 rigid closed tank contains 10 kg of water (in any phase or phases) at 150°C. What is the pressure in the tank?

Solution:

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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?

Solution:

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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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