Energy in simple harmonic motion, kinetic and potential energies, simple pendulum and its time period - Question Bank

1. When the speed of a particle in SHM is zero, its energy is purely:
A) Kinetic
B) Potential
C) Both kinetic and potential
D) Zero
2. Which of the following factors does NOT affect the time period of a simple pendulum?
A) Length of the pendulum
B) Acceleration due to gravity
C) Mass of the bob
D) None of the above
3. The total energy of a simple harmonic oscillator is E. What is the kinetic energy when the displacement is A/2?
A) E/4
B) 3E/4
C) E/2
D) E
4. If the time period of a simple pendulum is T, and its length is increased by 24 cm, its time period becomes T + 1 second. The original length of the pendulum is:
A) 1 m
B) 1.5 m
C) 2 m
D) 2.5 m
5. The potential energy of a particle in SHM is maximum when the displacement is:
A) Zero
B) Amplitude / 2
C) Amplitude
D) 2 * Amplitude
6. For a particle in SHM, the kinetic energy is maximum when the velocity is maximum. This occurs at:
A) Extreme positions
B) Mean position
C) Half amplitude position
D) Any position
7. A simple pendulum has a time period of 4 seconds. If its length is increased by 3 times, what will be the new time period?
A) 2 seconds
B) 4 seconds
C) 8 seconds
D) 12 seconds
8. The energy in SHM is continuously converted between kinetic and potential forms. At any instant, the total energy is:
A) Equal to kinetic energy
B) Equal to potential energy
C) The sum of kinetic and potential energy
D) Zero
9. What is the time period of a simple pendulum of length 1 meter on the surface of the Earth (g ≈ 9.8 m/s²)?
A) 1.0 s
B) 1.5 s
C) 2.0 s
D) 2.5 s
10. In SHM, when the displacement is x, the potential energy is proportional to:
A) x
B) x^2
C) 1/x
D) 1/x^2
11. If the length of a simple pendulum is L and its time period is T, then a pendulum of length L/2 will have a time period of:
A) T/2
B) T/√2
C) T√2
D) 2T
12. The potential energy of a particle executing SHM is maximum when the particle is at:
A) The mean position
B) The extreme position
C) Half the amplitude
D) Any position
13. For a simple pendulum, the time period T is given by T = 2π√(L/g). If g is doubled, the new time period T' will be:
A) T/√2
B) T√2
C) T/2
D) 2T
14. Which statement is correct regarding the total energy of a simple harmonic oscillator?
A) It is maximum at the mean position.
B) It is minimum at the extreme positions.
C) It is constant throughout the motion.
D) It is zero at the mean position.
15. The time period of a simple pendulum is T. If it is made to oscillate in a liquid of negligible viscosity, its time period will:
A) Increase
B) Decrease
C) Remain the same
D) Become infinite
16. When the displacement of a particle in SHM is equal to half of its amplitude, the ratio of its kinetic energy to its potential energy is:
A) 1:1
B) 3:1
C) 1:3
D) 2:1
17. A simple pendulum's length is increased by 21 cm, and its time period increases from 2 seconds to 2.2 seconds. The original length of the pendulum is:
A) 90 cm
B) 100 cm
C) 110 cm
D) 120 cm
18. The total energy of a particle in SHM is proportional to:
A) Amplitude
B) Square of amplitude
C) Frequency
D) Square of frequency
19. If the amplitude of oscillation of a system in SHM is A, the maximum displacement from the mean position is:
A) 0
B) A/2
C) A
D) 2A
20. What is the unit of angular frequency (ω) for a simple pendulum?
A) Hertz (Hz)
B) Radians per second (rad/s)
C) Seconds (s)
D) Meters per second (m/s)
21. For a simple pendulum, the time period is directly proportional to:
A) Length
B) Square root of length
C) Square root of inverse of length
D) Square of length
22. In SHM, the average potential energy over one complete oscillation is equal to:
A) Zero
B) Total energy
C) Half of the total energy
D) Twice the total energy
23. In SHM, the average kinetic energy over one complete oscillation is equal to:
A) Zero
B) Total energy
C) Half of the total energy
D) Twice the total energy
24. The time period of a simple pendulum is T. If the mass of the bob is doubled, the new time period will be:
A) T/2
B) T
C) 2T
D) √2T
25. A simple pendulum has a time period of 2 seconds. If its length is increased by 1 meter, its time period becomes 3 seconds. The original length of the pendulum is approximately:
A) 0.75 m
B) 1.0 m
C) 1.5 m
D) 2.0 m
26. A body is performing SHM. Its total energy is E. At a displacement x = A/2 from the mean position, what is its kinetic energy?
A) 3E/4
B) E/4
C) E/2
D) E
27. For a particle executing SHM, the velocity is v = ω√(A^2 - x^2). The kinetic energy is KE = (1/2)mv^2. What is the expression for KE in terms of displacement x?
A) (1/2)mω^2(A^2 - x^2)
B) (1/2)mω^2(x^2 - A^2)
C) (1/2)mω^2(A^2 + x^2)
D) (1/2)mω^2A^2
28. If a pendulum clock is taken to a place of higher altitude, its time period will:
A) Increase
B) Decrease
C) Remain the same
D) Become infinite
29. The maximum potential energy of a particle in SHM is equal to:
A) (1/2)kA^2
B) kA^2
C) (1/2)mω^2A^2
D) mω^2A^2
30. The maximum kinetic energy of a particle in SHM is given by:
A) (1/2)kA^2
B) kA^2
C) (1/2)mω^2A^2
D) mω^2A^2
31. A simple pendulum has a time period T. If its length is increased such that its time period becomes 2T, what is the factor by which the length has increased?
A) 2
B) √2
C) 4
D) 1/2
32. In SHM, the total energy is the sum of kinetic and potential energies. At any point, E = KE + PE. Which statement is always true about E?
A) E is zero
B) E is maximum
C) E is constant
D) E varies with displacement
33. If the frequency of a SHM is f, what is its time period T?
A) T = 1/f
B) T = f
C) T = 2πf
D) T = f/(2π)
34. The kinetic energy of a particle in SHM is zero at:
A) The extreme positions
B) The mean position
C) Half the amplitude
D) Any position
35. The potential energy of a particle in SHM is zero at:
A) The extreme positions
B) The mean position
C) Half the amplitude
D) Any position
36. If the mass of the bob of a simple pendulum is increased, what happens to its time period?
A) Increases
B) Decreases
C) Remains the same
D) Becomes zero
37. What is the angular frequency (ω) of a simple pendulum of length L?
A) √(L/g)
B) √(g/L)
C) g/L
D) L/g
38. For a simple pendulum, if the length is halved, how does the time period change?
A) It remains the same
B) It decreases by a factor of √2
C) It increases by a factor of √2
D) It doubles
39. The total energy of a system in SHM is conserved if:
A) There is friction
B) There are external driving forces
C) There are no non-conservative forces acting on the system
D) The amplitude decreases with time
40. When is the potential energy of a particle in SHM equal to its kinetic energy?
A) Only at the extreme positions
B) Only at the mean position
C) At positions where the displacement is ± A/√2
D) Never
41. The kinetic energy of a particle in SHM is maximum when the particle is at:
A) The extreme position
B) The mean position
C) Half the amplitude
D) Any position
42. If a simple pendulum is taken to the Moon where the acceleration due to gravity is approximately 1/6th of that on Earth, how will its time period change?
A) It will decrease
B) It will increase
C) It will remain the same
D) It will become zero
43. What is the formula for the time period (T) of a simple pendulum of length L in a location with acceleration due to gravity g?
A) T = 2π * sqrt(g/L)
B) T = 2π * sqrt(L/g)
C) T = sqrt(L/g)
D) T = 2π * (L/g)
44. The time period of a simple pendulum depends on which of the following quantities?
A) Mass of the bob and amplitude
B) Length of the string and acceleration due to gravity
C) Length of the string and mass of the bob
D) Acceleration due to gravity and amplitude
45. For a simple pendulum, the time period (T) is approximately 2.0 seconds. If the length of the pendulum is increased by a factor of 4, what will be the new time period?
A) 1.0 second
B) 2.0 seconds
C) 4.0 seconds
D) 8.0 seconds
46. If the amplitude of a SHM is doubled, how does the total energy of the system change?
A) It remains the same
B) It doubles
C) It quadruples
D) It halves
47. The potential energy of a particle executing SHM is given by U = (1/2)kx^2, where k is the spring constant and x is the displacement from the mean position. What is the nature of this potential energy?
A) Linear
B) Quadratic
C) Exponential
D) Logarithmic
48. For a system undergoing SHM, which of the following statements about the total mechanical energy is correct?
A) Total energy is proportional to the amplitude squared
B) Total energy is inversely proportional to the amplitude squared
C) Total energy is constant and independent of amplitude
D) Total energy varies with time
49. When an object is at the mean position in SHM, what is the state of its kinetic energy and potential energy?
A) KE is maximum, PE is zero
B) KE is zero, PE is maximum
C) KE and PE are equal
D) KE and PE are zero
50. In Simple Harmonic Motion (SHM), what is the relationship between kinetic energy (KE) and potential energy (PE) at the extreme positions of the oscillation?
A) KE is maximum, PE is zero
B) KE is zero, PE is maximum
C) KE and PE are equal
D) KE and PE are zero
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