# Length Contraction Formula

Length contraction is considered when an object has traveled with the velocity of light. So, relativity arrives into the picture. Therefore, one can say that length contraction happens when an object is traveling at the speed of light. This is described as the decrease in length if a body is traveling with the velocity of light linked to the observer. The formula for length contraction is articulated as,

$\dpi{120}&space;\large&space;L=L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}}$

Where, L is the length of an object with is in relativistic speed, L0 is the length of an object at rest, c is the velocity of light and  v is the velocity of the object.

Length Contraction Solved Examples

Solved problems of given topic are described underneath:

Problem 1: Compute the contracted length of an object whose initial length 10m and travel with a velocity 0.75c?

Given parameters are,
L0L0 = 10m and v = 0.75c
Formula for length contraction is,

$\dpi{120}&space;\large&space;10\times\sqrt{1-\frac{0.75c^{c}}{c^{2}}}$

$\dpi{120}&space;\large&space;10\times\sqrt{1-0.75^{2}}$

10x 0.6614=6.614 m

Problem  2: If L0 is 15m and velocity is 0.85c, compute the length contraction of a given object?
$\dpi{120}&space;\large&space;15\times\frac{\sqrt{1-(0.85c)^{2}}}{c^{2}}$
$15\times\sqrt{1-0.85^{2}}$