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…

### Harmonic Oscillations

Q- A harmonic force F_{0 }sin(ωt) is applied to mass m_{1} which in turn is coupled to springs of spring constants k_{1, }k_{2} and k_{3}. Let x_{1} and x_{2 }be the deviations from equilibrium for m_{1 }and m_{2}, respectively. The blocks moves on a horizontal frictionless table.

(a) Write the equations of motion for …

### 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…

### 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/r^{3}.

(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…

### 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…

### 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…

### Standing Waves: Vibrating string

Q- Figure shows the standing wave on a string, oscillating at frequency f_{o}.

(a) How many antinodes will there be if the frequency is doubled to 2f_{o}.

(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…

### Kinematics: Projectile Motion

Q- A rocket is fired at an angle of 60^{0} 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 …

### 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…

### 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/m^{3} and that of water is 1000 kg/m^{3}.

(a) calculate the …

### 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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