intro
Question 1:
What is the change in the time period if the length of a second pendulum is quadrupled?
Topic: Oscillation and Time Period in Physics
Correct Answer: D) Two-fold increase
- The time period of a pendulum is greatly influenced by its length.
- A pendulum's time period is proportional to its square root.
- As a result, if we increase the pendulum length by a factor of four, the time period will be doubled.
- Therefore, the correct answer is D, a "Two-fold increase."
Question 2:
What is the proportion of potential energy to total energy for a simple harmonic oscillator when it is at half its amplitude?
Topic: Energy Distribution in Harmonic Oscillations
Correct Answer: D) 25%
- In a simple harmonic oscillator, kinetic energy and potential energy combine to form total energy.
- One-fourth of the total energy is stored as potential energy when the oscillator's amplitude is half.
- Therefore, the correct answer is D, "25%".
Question 3:
If a simple pendulum is suspended from the ceiling of a lift in free fall, what frequency will it have?
Topic: Oscillations in Zero Gravity
Correct Answer: A) Zero
- The frequency of a simple pendulum is dependent on gravity.
- In a free-falling lift, the effective gravity becomes zero, thereby causing the pendulum to stop oscillating.
- Therefore, the correct answer is A, "Zero".
Question 4:
What would be the time period of a spring oscillating with a period of 12s on Earth, if it were taken to the Moon?
Topic: Oscillations in Different Gravitational Fields
Correct Answer: B) 12s
- The time period of a spring oscillator is independent of the gravitational field, it depends solely on the mass of the object and the spring constant.
- Therefore, even if the spring is taken to the moon, the time period remains unchanged.
- Hence, the correct answer is B, "12s".
Question 5:
If a pendulum bob executing simple harmonic motion has a velocity of "v" at its mean position, what will be its velocity if the amplitude is doubled, while keeping the length constant?
Topic: Velocity Dependence on Amplitude in Simple Harmonic Motion
Correct Answer: C) 2v
- The velocity of a body performing simple harmonic motion at the mean position is given by the equation v0 = x0ω.
- In this equation, v0 is directly proportional to x0 (the amplitude), provided the angular frequency ω remains constant.
- Therefore, if the amplitude is doubled, the velocity will also double.
- Hence, the correct answer is C, "2v".
Question 6:
In simple harmonic motion (SHM), when the kinetic energy is at its peak, which of the following statements is accurate?
Topic: Energy Characteristics in Simple Harmonic Motion
Correct Answer: D) All of the above
- Kinetic energy is maximized at the average position, which corresponds to zero displacement in simple harmonic motion.
- At this point, as all the energy is kinetic, the potential energy is zero.
- Furthermore, the acceleration is also zero at the mean position because the object is at maximum speed and changes direction without speeding up or slowing down.
- Thus, the correct answer is D, "All of the above".
Question 7:
What is the total distance covered by the bob of a simple pendulum in one complete oscillation?
Topic: Distance Travelled in One Oscillation of a Simple Pendulum
Correct Answer: D) Four times the amplitude
- The total distance travelled by a bob in one complete oscillation (or vibration) is the path from one extreme to the other and back.
- This path is four times the amplitude of the pendulum.
- Therefore, the correct answer is D, "Four times the amplitude".
Question 8:
Imagine a situation where a tunnel is dug straight through the Earth's center and a spherical object is dropped into it. How long would it take for this object to oscillate back and forth?
Topic: Oscillation of an Object in a Hypothetical Tunnel through the Earth
Correct Answer: D) 84.6 minutes
- This problem is theoretically based on the principle of simple harmonic motion (SHM).
- If an object moves along the circumference of a circle with constant angular velocity, its projection on the diameter of the circle would be executing SHM.
- Therefore, the time period of this SHM is equivalent to the time period of a particle moving along the circle.
- The given situation is analogous to a low orbiting satellite around the Earth, which has a time period of approximately 84 minutes.
- Consequently, the correct answer is D, "84.6 minutes".
Question 9:
Suppose x stands for displacement, v for velocity, and a for acceleration of an object executing simple harmonic motion with a time period of T. Which of these expressions remains constant over time?
Topic: Constants in Simple Harmonic Motion
Correct Answer: A) aT/x
- For an object undergoing SHM, the acceleration (a) is proportional to the displacement (x) and is also inversely proportional, given by the equation -ω2x, where ω2 is a constant.
- So, the term a/x becomes a constant.
- Since the time period T is also a constant, the expression aT/x also remains constant over time.
- Hence, the correct answer is A, "aT/x".
Question 10:
When a particle undergoes simple harmonic motion, what is the mathematical expression for its maximum velocity?
Topic: Maximal Velocity in Simple Harmonic Motion
Correct Answer: D) Expression D
- The maximum velocity in simple harmonic motion is reached when the object is at the mean position.
- The mathematical representation of this maximum velocity is given by the equation under consideration.
- Hence, the correct answer is D, "Expression D".
Question 11:
Given a particle performing Simple Harmonic Motion, which shape does the graph of velocity versus displacement form?
Topic: Graphical Representation of Velocity and Displacement in SHM
Correct Answer: C) An ellipse.
- When studying a body undergoing SHM, the shape of various graphs reveal significant insights.
- A graph plotting velocity against displacement forms an ellipse.
- Other graph representations include kinetic energy/potential energy versus displacement (parabola), total energy versus displacement (straight line), force/acceleration versus displacement (straight line), and displacement versus time (sinusoid).
- Therefore, the correct answer is C, "An ellipse".
Question 12:
When a mass m is hung from a perfect spring with force constant k, it oscillates. How would you describe its natural angular frequency?
Topic: Natural Angular Frequency in Simple Harmonic Motion
Correct Answer: A) Expression A
- In simple harmonic motion, a mass suspended from a spring will oscillate with a specific natural angular frequency.
- The expression for this angular frequency is given in the options.
- The correct option is A, "Expression A".
Question 13:
Consider an object oscillating with amplitude "A". What is the distance travelled by the object during one full cycle of its oscillation?
Topic: Distance Covered by an Oscillating Body
Correct Answer: D) 4A
- The total distance an oscillating body covers during one full cycle, or vibration, is calculated in terms of its amplitude, "A".
- The complete oscillation includes the path from one extreme, through the mean position, to the other extreme, and back to the initial extreme.
- This total distance equals four times the amplitude (4A).
- Thus, the correct answer is D, "4A".
Question 14:
Suppose the mass connected to a spring is quadrupled. What effect does this have on the time period?
Topic: Effect of Mass Change on Time Period in SHM
Correct Answer: A) It doubles
- Time period and mass are directly proportional in simple harmonic motion.
- If the mass is multiplied by four (squared), the time period will be doubled.
- Hence, the correct answer is A, "It doubles".
Question 15:
What is the acceleration of a particle undergoing SHM at the mean position?
Topic: Acceleration at Mean Position in SHM
Correct Answer: D) Zero
- In Simple Harmonic Motion, the acceleration (a) is given by the equation a = -ω²x.
- At the mean position, the displacement x is zero, making the acceleration a = -ω²(0) = 0.
- Therefore, the correct answer is D, "Zero".
Question 16:
Which of the following reaches its peak at the mean position?
Topic: Maximum at Mean Position in SHM
Correct Answer: D) Kinetic Energy (K.E)
- In simple harmonic motion, different quantities reach their maximum at different points.
- At the mean position, the kinetic energy is at its highest because the speed is maximum.
- Thus, the correct answer is D, "Kinetic Energy (K.E)".
Question 17:
A simple pendulum is set in motion within a stationary elevator and it takes 2 seconds to complete one oscillation. If the elevator begins to free fall, what would be the frequency of the pendulum's oscillations?
Topic: Frequency of Pendulum in Free Fall
Correct Answer: A) Zero
- The motion of a pendulum is dependent on the gravitational force acting upon it.
- If an elevator is in free fall, the effective gravitational force inside becomes zero.
- As a result, the pendulum would stop oscillating and the frequency of oscillations would fall to zero.
- Therefore, the correct answer is A, "Zero".
Question 18:
What is the frequency of a pendulum that completes one full swing in two seconds?
Topic: Frequency of a Second Pendulum
Correct Answer: C) 0.5 Hz
- Time period (T) and frequency (f) are inversely related. It is calculated as f = 1/T.
- For a pendulum that swings back and forth in 2 seconds, the frequency would be f = 1/2 = 0.5 Hz.
- Thus, the correct answer is C, "0.5 Hz".
Question 19:
What is the outcome when the frequency of an oscillation is multiplied by its time period?
Topic: Relationship Between Frequency and Time Period
Correct Answer: D) 1
- The time period (T) and frequency (f) of an oscillation are inversely proportional to each other, as given by the equation f = 1/T.
- Multiplying frequency by the time period results in fT = 1.
- Hence, the correct answer is D, "1".
Question 20:
Why is the average position of a simple harmonic motion (SHM) oscillator often referred to as the equilibrium position?
Topic: Equilibrium Position in SHM
Correct Answer: D) Both B and C are correct.
- The equilibrium position in Simple Harmonic Motion (SHM) is the point where the acceleration and displacement both equate to zero.
- As a body oscillates in SHM, it momentarily comes to rest at this position before reversing its direction of motion.
- Therefore, choice D, "Both B and C are correct", is the accurate answer.
Question 21:
How do the time periods of the same pendulum oscillating in Karachi and Murree compare?
Topic: Time Period of Pendulum at Different Altitudes
Correct Answer: C) Tk < TM
- The time period of a pendulum is inversely proportional to the square root of gravitational acceleration (g).
- Murree is at a higher altitude than Karachi, so g is slightly lower in Murree.
- Therefore, the pendulum will have a longer time period in Murree than in Karachi.
Question 22:
If the time period of a simple pendulum is given by 2π, what is its angular frequency?
Topic: Angular Frequency of a Simple Pendulum
Correct Answer: C) 1 Hz
- The angular frequency (ω) of a simple pendulum is given by ω = 2π/T, where T is the time period.
- Substituting T = 2π into the formula gives ω = 2π/2π = 1 Hz.
Question 23:
A pendulum is set into motion with a specific frequency 'f'. If regular and periodic forces are applied such that the amplitude of these oscillations doubles, what would be the new frequency?
Topic: Impact of Amplitude on Frequency of a Pendulum
Correct Answer: A) f
- A simple pendulum's frequency is determined by its length and gravitational acceleration, but not by its amplitude.
- Even if the amplitude is doubled by applying a series of regular pushes, the frequency remains the same.
- Thus, the correct answer is A, "f".
Question 24:
If a particle is moving uniformly along a circular path, its projection along the diameter of the circle would demonstrate which type of motion?
Topic: Projected Motion of a Particle Moving in a Circle
Correct Answer: C) Simple Harmonic Motion (SHM)
- When a particle moves uniformly along a circular path, the projection of its motion onto the diameter of the circle emulates Simple Harmonic Motion (SHM).
- This is because the projection's position, velocity, and acceleration change sinusoidally with time, which is a characteristic of SHM.
- Therefore, the correct answer is C, "Simple Harmonic Motion (SHM)".
Question 25:
When the absolute value of the displacement is equal to that of the acceleration, what is the time period of the motion?
Topic: Time Period in relation to Displacement and Acceleration
Correct Answer: C) 2π second
- In Simple Harmonic Motion (SHM), the acceleration 'a' is related to the displacement 'x' by the formula a = ω²x, where 'ω' is the angular frequency.
- Given that |a| = |x|, we can infer that ω² = 1, which simplifies to ω = 1.
- The time period 'T' of the motion can be found from ω = 2π/T, yielding T = 2π seconds when ω = 1.
- Therefore, the correct answer is C, "2π second".