Question

According to the Special Theory of Relativity, what happens to the length of an object as its velocity approaches the speed of light?

• A. It increases
• B. It decreases (length contraction)
• C. It remains unchanged
• D. It becomes infinite

Hint:

Relativistic length contraction: \[ L = L_0\sqrt{1-\frac{v^2}{c^2}} \] Objects moving close to the speed of light appear {shorter along the direction of motion}.

Answer 1

The Correct Option is B

Concept: According to Einstein's Special Theory of Relativity, the length of an object measured in the direction of motion appears shorter to an observer when the object moves at a velocity comparable to the speed of light. This phenomenon is known as length contraction. The relation for relativistic length contraction is \[ L = L_0 \sqrt{1-\frac{v^2}{c^2}} \] where

• \(L_0\) = proper length (length in the object's rest frame)
• \(L\) = observed length
• \(v\) = velocity of the object
• \(c\) = speed of light

Step 1: Analyze the velocity dependence.} As \(v\) approaches \(c\), \[ \frac{v^2}{c^2} \rightarrow 1 \] Thus, \[ \sqrt{1-\frac{v^2}{c^2}} \rightarrow 0 \]
Step 2: Conclusion.} Therefore, the observed length \(L\) becomes smaller than the proper length. Hence, the object appears contracted in the direction of motion.