Question

•At what speed does a meter stick move if its length is observed to shrink to 0.5 m?
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Answer 1

Answer:

Answer and Explanation:

In order to observe a meter stick to shrink its length to 0.5 meters, it must move at a speed of 2.6×108ms 2.6 × 10 8 m s .

Explanation:

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Answer 2

Concept:

The change in the length can be related to the velocity as

L = L₀ √(1 - (v²/c²))

where L is the length, L₀ is the initial length, v is the velocity of the stick and c is the velocity of the light.

Given:

The final length after shrinking the stick is 0.5 m.

Find:

The speed at which the meter stick is moving.

Solution:

Let the initial length of the stick be 1 m.

Calculating the velocity by substituting the given values,

L = L₀ √(1 - (v²/c²))

0.5 = 1 √(1 - (v²/c²))

Squaring on both sides,

(v²/c²)) = 1 - 0.5² = 1 - 0.25 = 0.75

Taking square root on both sides,

v = √0.75 c = 2.6 × 10⁸ m/s

Hence, the speed at which a meter stick move is  2.6 × 10⁸ m/s when the length is observed to shrink to 0.5 m.

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