asian institute of technology

Time: 1 hour 30 minutes
Admission Test
Additional materials: none
Attempt all questions.
The use of a non-programmable electronic calculator is allowed.
Section A (18 points)
1. A laser beam strikes one end of a slab of material with the length of L = 50 cm and the
thickness d = 4.7 mm. The index of refraction of the slab is 1.48. Determine the number
of internal refractions of the beam before it emerges from the opposite end of the slab.
2. Suppose that you have only 100 kΩ resistors and 50kΩ resistors but in your circiut you
need a 81.25 kΩ resistor. Make the required resistor value from the available resistors by
specifying the resistor values in the following circuit diagram.
3. A perfectly elastic canon ball is shot in the horizontal direction from a height h with an
initial velocity of 10 m/s. From how high above the impact point with the ground do we
need to shoot so the canon ball hits the ground under an angle of 45º. How far away from
the first impact in the horizontal direction and to what maximum height will the ball
rebounce when it impacts the ground for the second time. Assume that there is no air
friction and that the impacts with the ground are perfectly elastic.
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4. Two objects A and B are connected by a rigid rod that has a length L. The objects slide
along perpendicular guide rails, as shown in figure. If A slides to the left with the constant
speed vA;
(a) Find the velocity of B in the function of angle.
(b) Describe vB relative to vA. Hint: Is vB smaller or larger or same as vA?
5. The monochromatic light passes through two slits. As a result, the interference pattern
occurs on the screen with the third bright fringe appearing at point P on the screen which
is placed L distance apart from the slit. Once the screen is moved to 2L distance, what
fringe will occur at point P?
6. The first heater takes time t1 to heat an amount of water to its boiling point. The second
heater takes time t2 to heat a similar amount of water to its boiling point. If both heaters
are used to heat the same amount of water, how long will it take? (Assume that same
initial temperature in all three situations. Ignore the heat capacity of the container and the
heat loss to the environment)
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Section B (32 Points)
7. Roughly design the +5V dc supply circuit from the main line with 220V ac using a 5V
regulator. Draw the voltage waveform diagram for each step and explain briefly how it
works. You need not calculate the exact component value just assume reasonable values
for capacitors, inductors and resistors that you use.
8. A mass m is connected to the point O by means of a linear spring with spring constant k
and initial undeformed length L. The spring and the mass are set in uniform rotation in a
horizontal plane with angular velocity ω around point O. Discuss the possible
corresponding motion and radial position of the mass m in function of the values of m, k,
L and ω. Also compute the energy required to generate the motion.
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