Question

A meter stick moves in the direction of its length through a laboratory. According to measurements taken in the laboratory, it's length is .31 m. The speed of the meter stick relative to the laboratory is:

A) 0.096c
B) 0.31c
C) 0.69c
D) 0.83c
E) 0.95c

Answer 1

Correct option: option E. The moving meter stick experiences length contraction, which is a phenomenon of special relativity where objects moving at high speeds appear shorter in the direction of motion. By using the length contraction formula, the speed at which the meter stick's length contracts to 0.31 meters is found to be approximately 0.95 times the speed of light.

Step-by-step explanation:

This problem involves the concept of length contraction in special relativity.

Length contraction occurs when an object is moving relative to an observer at a significant fraction of the speed of light (c).

The formula for length contraction is L = L√(1 - v²/c²), where L is the contracted length, L is the proper length (the length of the object in its own rest frame), v is the relative velocity, and c is the speed of light.

In this case, we need to find the speed v at which a meter stick appears to be 0.31 meters in length in the laboratory frame.

The equation for length contraction can be rearranged to solve for v:

L = L√(1 - v²/c²)

0.31 = 1 √(1 - v²/c²)

0.31² = (1 - v²/c²)

1 - (0.31)^2 = v²/c²

v²/c² = 1 - (0.31)^2

v² = c²(1 - (0.31)^2)

v = c √(1 - (0.31)^2)

When you calculate this, you find that v is approximately 0.95c, which corresponds to option E.