As a fraction of c, the length will be 60% at v/c = 0.76
The length of the moving rod = 60%
Using the formula for length contraction-
L = L_o(√(1 - (v²/c²))
Where;
v = The speed of the object
c = The speed of light
L = The length of the object at a moving speed
L_o = The length of the object at rest
Thus,
L = 65%
L_o = 0.65
Substituting the values -
0.65L_o = L_o[√(1 - (v²/c²))]
Dividing both sides by L_o -
0.65 = √(1 - (v²/c²))
Squaring both sides -
0.65² = (1 - (v²/c²))
v²/c² = 1 - 0.65²
v²/c² = 0.5775
Taking the square root of both sides gives;
v/c = 0.76
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