Length contraction is described by L = L0/γ. If a rod has proper length L0, what is its length L as observed by a moving observer?

Length contraction is described by L = L0/γ. If a rod has proper length L0, what is its length L as observed by a moving observer?

• A. L = γ L0
• B. L = L0
• C. L = γ / L0
• D. L = L0 / γ

Answer: (D)

Length contraction says a rod moving relative to you appears shorter along its direction of motion. The amount of shortening is determined by the Lorentz factor γ = 1/√(1 − v²/c²), so the observed length is L = L0/γ, where L0 is the rod’s proper length measured in its own rest frame. The key point is that measuring the ends at the same instant in your frame leads to a shorter separation than when the rod is at rest, and γ > 1 makes L smaller than L0. As the speed v approaches c, γ grows without bound, so the observed length shrinks toward zero. So the correct relationship is L = L0/γ. The other forms would imply length grows with speed, or equal to the rest length, or mix up the units—none describe length contraction correctly.

Length contraction says a rod moving relative to you appears shorter along its direction of motion. The amount of shortening is determined by the Lorentz factor γ = 1/√(1 − v²/c²), so the observed length is L = L0/γ, where L0 is the rod’s proper length measured in its own rest frame. The key point is that measuring the ends at the same instant in your frame leads to a shorter separation than when the rod is at rest, and γ > 1 makes L smaller than L0. As the speed v approaches c, γ grows without bound, so the observed length shrinks toward zero.

So the correct relationship is L = L0/γ. The other forms would imply length grows with speed, or equal to the rest length, or mix up the units—none describe length contraction correctly.