Question

find the velocity with which a body should travel so that its length becomes half of the rest length
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Answer 1

At V = 0.866c or 86.6 % speed of light, the length of the body will become half of its proper length.

Explanation:

The formula is  

L = Lo √1 - v^2 / c^2

Here  

• L is the length observed by an observer when the object is in motion.
• Lo is the proper length.
• v is the relative velocity between the observer and the moving object.
• c is the speed of light.

Now L = Lo/2

Put the value to solve.

√(1− (v/c)^2 =1 / 2  

Taking square on both sides.

1 − (v / c)^2 = 1 / 4  

(v / c)^2 = 3/4  

v^2 = (3 / 4) x c^2  

V  = √(3)/2 x c

V = 0.866 c  

Thus at V = 0.866c the length of the body will become half of its proper length.

Answer 2

Answer:

The relativistic mass is given as m=

2

1−

c

2

v

2

m

0

Where m

0

is the rest mass and v is the velocity of that particle.

Putting m=2m

0

and squaring both side we get

c

2

v

2

=

4

3

now taking square root of both side we get v=

2

c

2

3