Question

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,
A. is not affected by the motion.
B. approaches infinity.
C. decreases due to the motion.
D. increases due to the motion.

Answer 1

The length of the train, as measured by a stationary observer on the ground decreases due to the motion.

Answer: Option C

Explanation:

According to Einstein's special theory of relativity, an observer in an inertial frame of reference will observe a decrease in the length of any moving object placed at another inertial frames of references. This process is termed as Length contraction.

So if L' is the proper length of the moving object or we can say the length the train at rest or original length of the train at rest. Then when it is in motion, the length of the train observed by the observed in another frame will be represented as L. And the relation between them can be known from Einstein's special theory of relativity as below,

                             $L=L^{\prime} \times \sqrt{1-\frac{v^{2}}{c^{2}}}$

So here v is the velocity of moving train and c is the velocity of light.  As at rest, the train's length will be L'.

When the train moves with its speed approaching the light's speed, then the length of the moving train observed by the stationary observer is found to decrease along with motion. As v tends to c, the length observed by the observer L will tend to zero with increase in the speed of the train to speed of light.