Special Theory of Relativity

Physics · 11th Class (Intermediate Part 1) · BISE Lahore

70 questions

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Special Theory of Relativity Test

10 questions · Special Theory of Relativity × 10

Sample questions

Showing 20 of 70 questions from this chapter. The full bank is in the chapter test below.

1
A frame of reference is best described as
- A.a device for measuring the speed of light
- B.the path followed by a moving body
- C.a coordinate system relative to which measurements are taken (correct answer)
- D.a set of clocks that always read the same time
Why: A frame of reference is any coordinate system - a room, a laboratory, a moving train, or a star field - relative to which positions and measurements are made. It is a coordinate system, not a measuring instrument or a path.
2
An inertial frame of reference is a coordinate system in which
- A.the law of inertia is valid (correct answer)
- B.the speed of light is zero
- C.every body remains permanently at rest
- D.gravity has no effect on bodies
Why: In an inertial frame a body at rest stays at rest and a body in uniform motion keeps moving in a straight line unless an unbalanced force acts on it, which is the law of inertia. Bodies in such a frame are not all at rest, so the third option is wrong.
3
Which of the following is a non-inertial frame of reference?
- A.a laboratory at rest on the Earth
- B.a car moving with uniform velocity along a straight road
- C.a spaceship coasting far from any star with constant velocity
- D.a car that is braking to a stop (correct answer)
Why: A braking car is accelerating, so a body inside it no longer stays at rest in the car's frame. Every frame that is accelerating or decelerating relative to an inertial frame is non-inertial.
4
The Earth is usually treated as an inertial frame of reference even though it rotates and revolves because
- A.it moves with a very large uniform velocity
- B.its acceleration is relatively small (correct answer)
- C.gravity does not act inside it
- D.the law of inertia fails only near the poles
Why: Strictly the Earth is non-inertial because of its rotation and revolution, but its acceleration is small enough that it is treated as inertial for ordinary measurements.
5
A ball is released inside a train that is moving with uniform velocity. For an observer inside the train, the ball falls
- A.along a parabolic path
- B.straight down to the point directly below its release point (correct answer)
- C.behind the point of release
- D.towards the front of the compartment
Why: The ball and the train share the same horizontal velocity, so in the train's frame the ball simply falls vertically and lands directly below the point of release.
6
A ball is let go from rest inside a train that is moving with uniform velocity. Described by a person standing beside the track, the path of the ball is
- A.a straight vertical line
- B.a vertical line and then a horizontal line
- C.a single point in mid-air
- D.a curved projectile path (correct answer)
Why: The ball keeps the horizontal velocity of the train, so the ground observer sees it behave like a projectile and trace a parabola. The vertical fall is the same in both frames, but the horizontal motion is seen only from the ground.
7
Throwing a ball to your right appears to a person facing you as going to his left. This example shows that
- A.direction is a relative concept (correct answer)
- B.the ball changes its speed from observer to observer
- C.motion is absolute
- D.the ball accelerates sideways when it is thrown
Why: The same motion is described as rightward by one observer and leftward by another, so direction - and hence rest and motion - is relative to the observer's frame of reference.
8
A traveller standing in the middle of a moving train compartment switches on a lamp fixed at the centre of the roof; the light opens the doors at both ends of the compartment. The traveller sees
- A.only the front door open
- B.only the rear door open
- C.both doors open simultaneously (correct answer)
- D.neither door open
Why: In the train's frame the light travels equal distances forwards and backwards at the same speed, so it reaches both doors together and the traveller sees them open at the same instant.
9
A train moving at half the speed of light has a lamp at the centre of the roof of a compartment, and the light from it opens doors at the two ends. An observer standing on the ground sees
- A.both doors open at the same instant
- B.the front door open first
- C.the lamp light reach both doors together
- D.the rear door open first (correct answer)
Why: While the light spreads out, the rear door moves towards the approaching light waves and the front door moves away from them, so the light reaches the rear door first.
10
The second postulate of the special theory of relativity states that
- A.the laws of physics are the same in all inertial frames
- B.mass and energy are interconvertible
- C.the speed of light in free space is the same for all observers, whatever the state of motion of the source or the observer (correct answer)
- D.time intervals are the same for all observers
Why: This is the principle of the constancy of light. The statement that the laws of physics are the same in all inertial frames is the first postulate, and mass-energy equivalence is a consequence of the theory, not a postulate.
11
If the laws of physics were different for observers in relative motion, then
- A.the speed of light would still be constant for both
- B.an observer could determine whether he was stationary or moving (correct answer)
- C.no observer could make any measurement
- D.time would become absolute
Why: Observers could then compare results and tell who was 'really' moving. Because no such difference is found, absolute uniform motion cannot be detected, which is what the first postulate asserts.
12
The theory of relativity that deals with frames of reference accelerating relative to one another is
- A.the general theory of relativity (correct answer)
- B.the special theory of relativity
- C.the relativistic mechanics of inertial frames
- D.Newtonian mechanics
Why: The special theory is restricted to inertial (non-accelerating) frames; the general theory extends relativity to accelerating frames and to gravity.
13
The speed of light in free space is
- A. $3 \times 10^{8}\ \mathrm{m\,s^{-1}}$ (correct answer)
- B. $3 \times 10^{6}\ \mathrm{m\,s^{-1}}$
- C. $3 \times 10^{5}\ \mathrm{m\,s^{-1}}$
- D. $3 \times 10^{10}\ \mathrm{m\,s^{-1}}$
Why: Light travels at $3 \times 10^{8}\ \mathrm{m\,s^{-1}}$ , that is 300,000 km per second. The value $3 \times 10^{5}$ is the same speed wrongly expressed in metres per second instead of kilometres per second.
14
A driver switches on the headlights of a car moving with speed $v$ . The speed of the light measured by the driver and by a person standing on the road is
- A. $c + v$ for the driver and $c$ for the person on the road
- B. $c - v$ for the driver and $c$ for the person on the road
- C. $c + v$ for both
- D. $c$ for both (correct answer)
Why: The speed of light in free space is the same for every observer, independent of the motion of the source or of the observer, so both measure exactly $c$ .
15
A direct consequence of the speed of light being the same for all observers is that
- A.mass becomes an absolute quantity
- B.the laws of physics differ from frame to frame
- C.space and time become relative (correct answer)
- D.light requires a medium in which to travel
Why: Because every observer must obtain the same value of $c$ , measurements of distance and of time interval cannot be absolute - both depend on the relative motion of the observer and the events.
16
A person sitting in a train that moves at the speed of light holds a mirror at arm's length and still sees his reflection. This is because
- A.light travels faster inside the moving train
- B.no experiment can detect the constant motion of the train relative to the person inside it (correct answer)
- C.the mirror is also moving with the light
- D.reflection of light does not obey the laws of physics
Why: By the principle of relativity the person is at rest in his own inertial frame, so light behaves exactly as it does in a stationary room. Motion that is uniform cannot be detected by any experiment performed inside the frame.
17
If two events at different places are observed to be simultaneous by one observer, then another observer moving relative to the first will generally find them
- A.simultaneous as well
- B.simultaneous only if he moves at the speed of light
- C.not simultaneous (correct answer)
- D.impossible to observe
Why: Simultaneity is not absolute: whether two separated events are seen as simultaneous depends on the observer's frame of reference. Only events at the same place and time are simultaneous for every observer.
18
The proper time between two events is the time interval measured
- A.by a clock moving at relativistic speed
- B.by a clock at rest relative to the events (correct answer)
- C.by the observer who is moving fastest
- D.in any frame, because time is absolute
Why: Proper time $t_0$ is the time measured in the frame in which the two events occur at the same place, that is, by a clock at rest with respect to the events. It is the shortest time interval measured between those events.
19
If $t_0$ is the proper time between two events, the time $t$ measured by an observer moving with speed $v$ relative to those events is
- A. $t = t_0\left(1 - \frac{v^2}{c^2}\right)$
- B. $t = t_0\sqrt{1 - \frac{v^2}{c^2}}$
- C. $t = \frac{t_0}{1 - \frac{v^2}{c^2}}$
- D. $t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$ (correct answer)
Why: The dilated time is the proper time divided by $\sqrt{1 - v^2/c^2}$ , the factor by which time stretches. The option multiplying by $\sqrt{1 - v^2/c^2}$ would make the moving clock run fast, which is the opposite of what happens.
20
In the time dilation formula, the measured time $t$ is always longer than the proper time $t_0$ because
- A. $\sqrt{1 - \frac{v^2}{c^2}}$ is always less than 1 (correct answer)
- B. $\sqrt{1 - \frac{v^2}{c^2}}$ is always greater than 1
- C. $v$ is always greater than $c$
- D.the speed of light changes when the source moves
Why: For any speed $v < c$ the factor $\sqrt{1 - v^2/c^2}$ lies between 0 and 1, so dividing $t_0$ by it gives a larger value - time has stretched, or dilated.

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