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All questions of Equivalence Principle for EmSAT Achieve Exam

According to the Einsteinian interpretation, what happens to two apples in a falling elevator as it approaches Earth?
  • a)
    The apples move farther apart.
  • b)
    The apples remain stationary relative to each other.
  • c)
    The apples converge toward each other.
  • d)
    The apples oscillate due to gravitational waves.
Correct answer is option 'C'. Can you explain this answer?

In a falling elevator, both the elevator and the apples are in free fall, experiencing the same acceleration due to gravity. However, as the elevator approaches Earth, the gravitational force slightly varies with distance, causing the paths of the apples to converge toward the Earth's center. This convergence demonstrates how local experiments cannot fully reveal global gravitational effects, a core concept of the equivalence principle.

What is the weak equivalence principle primarily concerned with?
  • a)
    The equality of gravitational and inertial mass
  • b)
    The behavior of electromagnetic forces in free-fall conditions
  • c)
    The divergence of objects in a non-uniform gravitational field
  • d)
    The curvature of spacetime by massive objects
Correct answer is option 'A'. Can you explain this answer?

The weak equivalence principle focuses on the equivalence between gravitational and inertial mass. It asserts that the motion of freely falling bodies is independent of their composition or structure. This principle underpins the universality of free fall, as demonstrated by experiments involving various materials falling with identical acceleration under gravity.

Which experiment aims to test the universality of free fall (UFF) by investigating dark matter interactions with ordinary matter?
  • a)
    Experiments with Be, Al, Cu, and Si attracted by the Earth
  • b)
    Experiments with test bodies attracted toward the center of our Galaxy
  • c)
    Laser-ranging data for Earth and Moon falling toward the Sun
  • d)
    Tests using compact uranium attractors
Correct answer is option 'B'. Can you explain this answer?

Experiments involving test bodies attracted toward the center of our Galaxy aim to investigate whether the significant force between dark matter and ordinary matter is purely gravitational, adhering to the UFF. These experiments are designed to verify if dark matter behaves like other forms of matter under gravity, ensuring that no new forces exist that violate the equivalence principle.

Why are scalar charges not conserved under Lorentz transformations?
  • a)
    They depend on the velocity of the observer.
  • b)
    Their integral involves only charge density, which changes with reference frames.
  • c)
    Scalar charges are conserved only for massless particles.
  • d)
    Lorentz transformations do not affect scalar fields.
Correct answer is option 'B'. Can you explain this answer?

Scalar charges are not conserved under Lorentz transformations because the integral involves the charge density (a Lorentz scalar), which is integrated over a volume element that changes with reference frames. Unlike vector charges, which remain Lorentz invariant due to compensating factors in current density and volume element, scalar charges are dependent on the reference frame, leading to interesting variations in interactions based on relativistic effects.

What does the equivalence principle state about the relationship between gravitational and inertial mass?
  • a)
    They are unrelated and vary depending on the object.
  • b)
    They are equivalent, meaning the gravitational force experienced is proportional to inertial mass.
  • c)
    Gravitational mass is always greater than inertial mass.
  • d)
    Inertial mass only applies in non-gravitational interactions.
Correct answer is option 'B'. Can you explain this answer?

The equivalence principle asserts that gravitational mass (the charge interacting with gravity) and inertial mass (an object's responsiveness to acceleration) are equivalent. This equivalence implies that all objects fall with the same acceleration in a uniform gravitational field, as their inertial and gravitational masses cancel out. For example, near Earth's surface, this acceleration is approximately 9.8 m/s². This principle is fundamental to understanding the uniformity of gravitational behavior across all objects.

What type of experiment tests the equivalence principle by comparing the accelerations of test bodies toward the Sun?
  • a)
    Laser-ranging experiments involving the Earth and Moon
  • b)
    Experiments using compact uranium attractors
  • c)
    Tests with Be, Al, Cu, and Si attracted by the Sun
  • d)
    Measurements of dark matter interactions with ordinary matter
Correct answer is option 'C'. Can you explain this answer?

Experiments testing the equivalence principle often involve comparing the accelerations of different materials (e.g., Be, Al, Cu, and Si) toward the Sun. These tests aim to validate the universality of free fall and assess whether gravitational self-energy affects adherence to the equivalence principle. They complement laser-ranging data by isolating effects related to composition and gravitational binding energy.

Why was uranium chosen as the attractor in experiments testing the UFF at short ranges?
  • a)
    It has the highest gravitational binding energy.
  • b)
    Its density allows positioning a substantial mass close to the torsion balance.
  • c)
    It emits radiation detectable by experimental instruments.
  • d)
    It closely resembles the composition of Earth's core.
Correct answer is option 'B'. Can you explain this answer?

Uranium was selected for these experiments because of its high density, which enables a large mass to be placed near the torsion balance for testing short-range gravitational effects. These experiments help address the sensitivity gap in UFF tests at distances between 10 km and 1000 km, providing insights into short-range interactions and ruling out hypothetical fifth forces.

What distinguishes the strong equivalence principle from the weak equivalence principle?
  • a)
    The strong equivalence principle applies only to gravitational self-energy.
  • b)
    The strong equivalence principle extends to all laws of nature, not just free-fall behavior.
  • c)
    The strong equivalence principle is restricted to objects in vacuum.
  • d)
    The strong equivalence principle contradicts the weak equivalence principle in non-Lorentz frames.
Correct answer is option 'B'. Can you explain this answer?

The strong equivalence principle generalizes the weak equivalence principle by stating that all laws of nature, not just the behavior of freely falling bodies, hold true in locally inertial frames. It even incorporates gravitational self-energy into the framework, demonstrating a broader scope compared to the weak equivalence principle, which primarily focuses on the equality of inertial and gravitational mass.

Why could a vector field interacting with mass violate the equivalence principle?
  • a)
    It would require the existence of mass and antimass with opposite behaviors.
  • b)
    It would necessitate conservation of scalar charges.
  • c)
    It would ignore the effects of spacetime curvature.
  • d)
    It would invalidate the concept of locally Lorentz frames.
Correct answer is option 'A'. Can you explain this answer?

A vector field interacting with mass could violate the equivalence principle because vector fields generally have charges and anticharges. If a vector field coupled with mass, it would imply the existence of "antimass" behaving oppositely in a gravitational field. This behavior contrasts with the equivalence principle, which assumes uniformity in the response of all matter to gravity.

What is a significant experimental finding from tests of UFF involving Be, Al, Cu, and Si attracted by the Earth?
  • a)
    Variations in acceleration were detected due to composition differences.
  • b)
    Null results confirm no deviation from the equivalence principle.
  • c)
    The experiments indicated a new form of gravitational binding energy.
  • d)
    Differences in neutron-to-proton ratios led to observable effects.
Correct answer is option 'B'. Can you explain this answer?

Tests of UFF using materials such as Be, Al, Cu, and Si attracted by the Earth produced null results, meaning no deviations from the equivalence principle were observed. These findings support the universality of free fall and demonstrate that all objects, regardless of their composition, experience the same gravitational acceleration.

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