Question:medium

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

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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}.
Updated On: Mar 25, 2026
  • It increases
  • It decreases (length contraction)
  • It remains unchanged
  • It becomes infinite
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The Correct Option is B

Solution and Explanation

Step 1: Understanding the Concept:
One of the most famous consequences of Einstein's Special Theory of Relativity is that measurements of space and time are not absolute. They depend on the relative velocity between the observer and the object being measured.
Step 2: Key Formula or Approach:
The relativistic length contraction formula determines the observed length $L$:
\[ L = L_0 \sqrt{1 - \frac{v^2}{c^2}} \]
where $L_0$ is the proper length (length measured by an observer at rest relative to the object), $v$ is the relative velocity, and $c$ is the speed of light.
Step 3: Detailed Explanation:
Analyze the term inside the square root: $1 - \frac{v^2}{c^2}$.
As the velocity of the object $v$ increases and approaches the speed of light $c$, the fraction $\frac{v^2}{c^2}$ approaches $1$.
Consequently, the term $1 - \frac{v^2}{c^2}$ approaches $0$.
The square root of a value approaching zero also approaches zero.
Multiplying the proper length $L_0$ by a factor approaching zero means the measured length $L$ will approach zero.
Thus, the length of the object significantly decreases along the direction of motion as it approaches the speed of light. This phenomenon is called length contraction.
Step 4: Final Answer:
The correct option is (B).
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