Question

Find the velocity with which a body should travel so that its length becomes half of the rest length

Answer 1

Explanation:

is the length observed by an observer in motion relative to the object.

L0 is the proper length.

v is the relative velocity between the observer and the moving object.

c is the speed of light.

By solving this equation for L=L0/2

sqrt(1−(v/c)2))=1/2

1−(v/c)2=1/4

(v/c)2=3/4

v2=(3/4)∗c2

v=(sqrt(3))/2∗c

v=0.866c

Answer 2

If a body travels with speed v = 0.886 m/s then its length will become half.

Let's see how the length of the body will become half.

Step 1 :

Let's take the equation L = Lo √ 1 - v^2/ c^2

Here, L = length observed by the observer

L0 =  proper length.

v = relative velocity between the observer and the moving object.

c = speed of light

Step 2:

Solution:

L = Lo/ 2

√1 -(v/c)^2 = 1/2

√1 -(v/c)^2 = 1/4

(v/c)^2 = 3/4

v = 3/4 x c^2

v = 0.886 c

After solving we get v = 0.886 c.

Thus, we see that the length of the body will become half.