QCAA Physics Special relativity

Stability is determined by binding energy per nucleon, not total binding energy, so we cannot determine which nucleus is more stable without knowing their nucleon numbers.

Stability depends on binding energy per nucleon, which cannot be determined from total binding energy alone.

Since nucleus X has a greater binding energy, it must have a greater mass defect than Y, not the other way around.

This calculation incorrectly treats the given 125 m as the proper length ($L_0$) and solves for the contracted length. Since the observer on the spaceship is at rest relative to it, they measure the proper length, which must be longer than the contracted length measured by the outside observer.

This answer results from omitting the square root in the Lorentz factor calculation, dividing 125 by $(1 - 0.3^2)$ instead of $\sqrt{1 - 0.3^2}$.

This value is incorrect and does not align with the standard length contraction formula. It likely results from a calculation error or misapplication of the Lorentz factor $\gamma$.

Incorrect. Since the electron is already traveling close to the speed of light when $\gamma = 200$, its speed can only increase by a very small fraction to approach $c$.

Incorrect. The speed only increases by a small amount because it cannot exceed the speed of light, while the energy increases by a large amount.

Incorrect. The energy increases by a large amount because it is directly proportional to the Lorentz factor ($E = \gamma mc^2$), which increases tenfold from 200 to 2000.

This statement is factually incorrect and unrelated to special relativity. According to the quantum relation $E=hf$, energy is directly proportional to frequency, so energy decreases as frequency decreases.

This describes the Doppler effect rather than a fundamental postulate. While relativity influences the Doppler shift, the postulates specifically define the behavior of the speed of light, not the change in wavelength due to source motion.

This is incorrect regarding wave mechanics; frequency remains constant when light changes media, while speed and wavelength change. Furthermore, this is a concept of optics, not a postulate of special relativity.

This is incorrect because an accelerating object represents a non-inertial frame of reference. By definition, an inertial frame must have zero acceleration.

This is incorrect because turning a corner involves a change in direction, which means the car is experiencing centripetal acceleration. Even at a constant speed, a change in direction makes it a non-inertial frame of reference.

This is incorrect because the roller-coaster is speeding up, meaning its velocity is changing and it is accelerating. Any accelerating environment is a non-inertial frame of reference.

Length contraction occurs along the direction of motion, not necessarily the height, and it is a consequence of relativistic speed rather than a barrier preventing acceleration.

Time dilation describes the relative slowing of time in a moving frame; it does not actively decrease velocity or physically prevent an object from accelerating.

As an object approaches the speed of light, its effective inertia (resistance to acceleration) increases towards infinity, making it harder to accelerate, not easier.

This formula represents gravitational potential energy, where $g$ is the acceleration due to gravity and $h$ is the height above a reference point.

This is an incorrect variation that conflates the kinetic energy coefficient ($\frac{1}{2}$) with the speed of light ($c$).

This is the formula for classical kinetic energy, describing the energy of an object in motion with velocity $v$, rather than the energy equivalent of mass itself.

Incorrect. This value incorrectly calculates power by multiplying the mass rate by the speed of light ($c$) instead of $c^2$.

Incorrect. This option uses the incorrect formula ($mc$ instead of $mc^2$) and the wrong unit for power, which should be Watts, not Joules.

Incorrect. Although the numerical calculation is correct, the unit for power is Watts (Joules per second), not Joules.

This is incorrect because relativistic momentum is a concept in special relativity, not Newtonian mechanics. In a Newtonian framework, momentum is simply defined as $p=mv$ without the Lorentz factor.

Momentum is a frame-dependent quantity, meaning its value changes depending on the observer's velocity relative to the object. It cannot be defined regardless of the frame.

In the frame where the object is stationary (its rest frame), the velocity is zero, and therefore the momentum is zero. This does not define the general concept of relativistic momentum.

This value is lower than the calculated proper time derived from the time dilation formula.

This result incorrectly divides by the Lorentz factor ($15 / \sqrt{1-0.7^2} \approx 21$), implying time passes faster on the spaceship, whereas special relativity states moving clocks run slower.

This value suggests much more time passes on the spaceship than on Earth, contradicting the principle of time dilation where the moving observer experiences less time.