Tribhuvan University
Institute of Science and Technology
TU Exam Year: 2080
Candidates are required to give their answers in their own words as far as practicable.
SECTION A
Attempt all questions.
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1.
Distinguish rigid and non-rigid bodies. Derive an expression for rotational kinetic energy and discuss the conditions for conservation of energy. A wheel of radius 0.4 m and moment of inertia \( 1.2\ \text{kg}\cdot\text{m}^{2} \), pivoted at the center, is free to rotate without friction. A rope is wound around it and a 2-kg weight is attached to the rope. When the weight has descended 1.5 m from its starting position, find the rotational velocity of the wheel.
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2.
Set up the Schrödinger equation for the Hydrogen atom using spherical polar coordinates. Separate the radial and angular parts of this equation using an appropriate separation constant. Discuss the separation constant and hence the quantum numbers associated with these two equations. What information can be drawn from the angular part of the Schrödinger equation?
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3.
What are RTL and TTL gates? How can memory and clock circuits be made using these gates? Show it. Explain their working scheme. Are TTL logic gates typically fabricated onto a single integrated circuit (IC)?
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4.
Describe the classical free electron model.
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5.
How are electric and magnetic fields incorporated into electromagnetic waves?
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6.
Describe the following processes in IC production: (a) Oxidation and (c) Doping. Explain Photolithography in brief.
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7.
An oscillating block of mass 250 g takes 0.2 sec to move between the endpoints of the motion, which are 50 cm apart. Find the frequency and amplitude of the motion. What is the force constant of the spring?
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8.
A potential difference of 100 V is applied between two plates, one being at a high potential. An alpha particle of charge \( q = 3.2 \times 10^{-19}\ \text{C} \) is released from one plate to another. What will be the velocity of the alpha particle when it reaches the plate?
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9.
Calculate the uncertainty in the momentum of an electron if the uncertainty in its position is \( 1\ \text{\AA}\ (10^{-10}\ \text{m}) \).
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10.
A current of 50 A is supplied in a slab of copper 0.5 cm thick and 2 cm wide, placed in a magnetic field \( B = 1.5\ \text{T} \). The magnetic field is perpendicular to the plane of the slab and to the current. If the free electron concentration in copper is \( 8.4 \times 10^{28}\ \text{electrons/m}^3 \), what will be the magnitude of the Hall voltage across the width of the slab?
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11.
Sodium has a body-centered cubic structure with a one-atom basis. The density and atomic weight of sodium are \( 0.971\ \text{g/cm}^{3} \) and 23 g/mole, respectively. What is the length of the unit cube of the structure?
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12.
The output of a digital circuit \( y \) is given by this expression: \( y = (C + \overline{B}A)(\overline{A + B + D}) \). Where A, B, C, and D represent inputs. Draw a circuit of the above equation using OR, AND, and NOT gates and hence find its truth table.