Test: Special Theory of Relativity - EmSAT Achieve MCQ

According to classical physics, the inertial mass of a body is independent of the velocity of light. It is regarding as a constant. However special theory of relativity leads us to the concept of variation of mass with velocity. It follows from special theory of relativity that the mass m of a body moving with relativistic velocity v relative to an observer is larger than its m0 when it is at rest.

According to Einstein, the mass of the body in motion is different from the mass of the body at rest.

This is the relative formula for variation of mass with velocity where m₀ is the rest mass and m is the relativistic mass of the body.
Total energy = Rest energy + Kinetic Energy
Since E = mc²
mc² = m_oc² + KE
K E = (m – m_o) c²
This can be written as:

• The energy possessed by a body due to its motion is called Kinetic energy.
• Temperature is directly proportional to kinetic energy.
• If the temperature increases, then the kinetic energy of the particles also increases.
• Kinetic energy is usually measured in units of Joules(J).
• Kelvin(K) is the SI unit of temperature.

• No object or signal can move faster than the speed of light. 
• According to the special theory of relativity, which was developed by Albert Einstein in 1905.
• Space and time are relative, and all motion must be relative to a frame of reference, according to Albert Einstein's theory of relativity.

The correct answer is ​Kinetic Energy.

• The kinetic energy of an object is the energy that it possesses due to its motion.
• It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
• Kinetic energy can be transferred between objects and transformed into other kinds of energy.
• The amount of kinetic energy that an object has depends upon two variables i.e. the mass (m) of the object and the speed (v) of the object.
• The form of energy possessed by a horse running on a level road is kinetic-energy. 

• Momentum is a vector quantity; it has both magnitude and direction.
• Isaac Newton’s second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
• Momentum can be calculated by multiplying the mass of an object by its forward velocity. (mv = kg*m/s).
• Mass and velocity are both directly proportional to the Momentum.
  • If you increase either mass or velocity, the Momentum of the object increases proportionally.
  • If you double the mass or velocity, you double the Momentum.
  • If you halve the mass or velocity, you half the Momentum.
• Newton's laws of motion-
  • ​Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by force. This postulate is known as the law of inertia.
  • Newton’s second law is a quantitative description of the changes that a force can produce in a body's motion. It states that the time rate of change of a body's momentum is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity.
  • Newton’s third law states that when two bodies interact, they apply forces to one another equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing static equilibrium problems, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion.

The correct answer is The momentum of the bullet and the gun before firing would be zero.

• Before firing, the gun and the bullet are both at rest, so the momenta (mv) of the gun and the bullet are both zero.
• Hence, the total momentum of the system before the bullet is fired is zero. So, option 1 is correct.

• There are many unique ideas in the special theory of relativity.
• The one about the speed of light is
  • The speed of light in the vacuum is completely independent of the observer's motion.
  • It means the speed of light will always be constant for all frames of reference.
• So, the correct answer will be option 2.

Given particle is electron, the mass of electron is m = 9.11 × 10^-31 kg, c = 3 × 10⁸ m/s

1 eV = 1.602 × 10-19 J

E = 2 MeV = 2 × 10⁶ × 1.602 × 10^-19 J = 3.204 × 10^-13 J 

Now from the above formula:

An astronaut at rest has a heart rate of 65 beats/min. When the astronaut’s spaceship moves at a speed of 0.6 c, her heart rate as measured by an earth observer will be:

frequency, f = 65 beats per minute.

In one minute there are 65 beats.

T = 1/65 min, v = 0.6 c

T' = in one minute, 52 beats

T' = 52 beats/min