1. A particle of mass m and charge q is accelerated from rest through a potential difference V. What is the magnitude of its final momentum?
Solution
Correct: A
The kinetic energy gained by the particle is qV. Thus, 1/2 mv² = qV, so v = √(2qV/m). The momentum is then p = mv = m√(2qV/m) = √(2mqV).
2. A long solenoid with n turns per unit length carries a current I. What is the magnetic field strength inside the solenoid?
Solution
Correct: A
The magnetic field inside a long solenoid is given by B = μ₀nI, where n is the number of turns per unit length and I is the current.
3. Two identical loudspeakers are placed a distance d apart. They emit sound of wavelength λ in phase. At what angles θ relative to the perpendicular bisector of the line joining the speakers will constructive interference occur?
Solution
Correct: A
For constructive interference, the path difference d sin(θ) must equal an integer multiple of the wavelength, nλ. Therefore, d sin(θ) = nλ, so sin(θ) = nλ/d, and θ = sin⁻¹(nλ/d).
4. A radioactive sample has a half-life of T. What fraction of the original sample remains after a time of 3T?
Solution
Correct: A
After one half-life (T), 1/2 remains. After two half-lives (2T), 1/2 * 1/2 = 1/4 remains. After three half-lives (3T), 1/2 * 1/2 * 1/2 = 1/8 remains.
5. What is the de Broglie wavelength of an electron with kinetic energy K?
Solution
Correct: A
The de Broglie wavelength is λ = h/p, where p is the momentum. Kinetic energy K = p²/2m, so p = √(2mK). Therefore, λ = h/√(2mK).
6. Two resistors, R₁ and R₂, are connected in parallel. The equivalent resistance of the parallel combination is:
Solution
Correct: A
For resistors in parallel, 1/R_eq = 1/R₁ + 1/R₂. Solving for R_eq gives R_eq = R₁R₂ / (R₁ + R₂).
7. A photon has an energy of 3.0 eV. What is its wavelength?
Solution
Correct: A
E = hc/λ, so λ = hc/E. Using h = 4.14 x 10⁻¹⁵ eV s and c = 3 x 10⁸ m/s, λ = (4.14 x 10⁻¹⁵ eV s * 3 x 10⁸ m/s) / 3.0 eV = 4.14 x 10⁻⁷ m = 414 nm.
8. A mass m is attached to a spring with spring constant k. The mass is displaced a distance A from equilibrium and released. What is the maximum speed of the mass?
Solution
Correct: A
The total energy is 1/2 kA². At the equilibrium position, all potential energy is converted to kinetic energy, so 1/2 kA² = 1/2 mv². Thus, v = A√(k/m).
9. What is the SI unit of magnetic flux?
Solution
Correct: A
The SI unit of magnetic flux is the Weber (Wb). Tesla is the unit of magnetic field strength.
10. The electric potential at a point is 10 V. What is the work done in bringing a charge of 0.1 C from infinity to that point?
Solution
Correct: A
Work done = qV = 0.1 C * 10 V = 1 J.
11. A car is moving with a velocity v. If the momentum of the car doubles, what happens to its kinetic energy?
Solution
Correct: A
Kinetic energy is K = p²/2m. If p doubles, the kinetic energy becomes (2p)²/2m = 4p²/2m = 4K. Therefore, the kinetic energy quadruples.
12. What is the period of a simple pendulum of length L on the surface of a planet with gravitational acceleration g?
Solution
Correct: A
The period of a simple pendulum is given by T = 2π√(L/g).
13. An ideal gas undergoes an isothermal process. Which of the following remains constant?
Solution
Correct: A
In an isothermal process, the temperature remains constant. Since internal energy (U) for an ideal gas is directly proportional to temperature (U = (3/2)nRT), internal energy also remains constant. Pressure and Volume will change.
14. What is the relationship between the object distance (u), image distance (v), and focal length (f) of a thin lens?
Solution
Correct: A
The thin lens equation is given by 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance.
15. Which of the following is NOT a fundamental force in nature?
Solution
Correct: A
The four fundamental forces are the strong nuclear force, the weak nuclear force, the electromagnetic force, and gravity. Tension is a macroscopic force arising from electromagnetic forces.
16. A diffraction grating has 500 lines per millimeter. What is the angle of the second-order maximum for light of wavelength 500 nm?
Solution
Correct: A
The grating spacing d = 1 / (500 lines/mm) = 2 x 10⁻⁶ m. The grating equation is d sin(θ) = nλ. For n = 2, sin(θ) = (2 * 500 x 10⁻⁹ m) / (2 x 10⁻⁶ m) = 0.5. Thus, θ = sin⁻¹(0.5) = 30 degrees.
17. What is the SI unit of capacitance?
Solution
Correct: A
The SI unit of capacitance is the Farad (F).
18. A particle is moving in simple harmonic motion. At what displacement from equilibrium is its potential energy equal to its kinetic energy?
Solution
Correct: A
Potential energy U = (1/2)kx², and total energy E = (1/2)kA². Kinetic energy K = E - U = (1/2)kA² - (1/2)kx². Setting U = K gives (1/2)kx² = (1/2)kA² - (1/2)kx², so x² = A²/2, and x = A/√2.
19. A transformer has 100 turns on its primary coil and 500 turns on its secondary coil. If the primary voltage is 120 V, what is the secondary voltage?
Solution
Correct: A
Vp/Vs = Np/Ns, where Vp is primary voltage, Vs is secondary voltage, Np is number of primary turns, and Ns is number of secondary turns. Therefore, Vs = Vp * (Ns/Np) = 120 V * (500/100) = 600 V.
20. What is the period of a wave with a frequency of 5 Hz?
Solution
Correct: A
The period (T) and frequency (f) are inversely related: T = 1/f. Therefore, T = 1/5 Hz = 0.2 s.
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