### All GRE Subject Test: Physics Resources

## Example Questions

### Example Question #1 : Length Contraction

A meter stick, at an angle of 30 degrees with the x-axis, is traveling at 0.6*c* in the direction of the positive y-axis. To a stationary observer, how long does the meter stick appear to be?

**Possible Answers:**

**Correct answer:**

Length contraction only occurs in the direction of motion. This means that the x component of the length, which is cos(30), does not change; length contraction only occurs the the y component, which is sin(30).

First, we find the Lorentz factor:

Next, we apply the time dilation equation to the length in the y direction:

Finally, we find the total length by combining the length-contracted y component and the unchanged x component:

### Example Question #2 : Length Contraction

A rocket of length 5 meters passes an observer on earth. The observer measures the passing rocket to be 3 meters long. What is the velocity of the rocket in the reference frame of the Earth-based observer?

**Possible Answers:**

**Correct answer:**

Length contraction is given by

Where in this case,

The Lorentz factor is given by:

Combining these two equations, we get:

Solving for v:

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