How long would a meterstick appear to be if it were traveling like a properly thrown spear at 99.5% the speed of light?
Solution 25RQ Introduction: In relativistic speeds, the length of an object is appeared to decreased when the observer or the object is travelling at non-zero velocity. This phenomenon is called as “length contraction” 2 The mathematical expression for length contraction is, L = L 0 1 c2 Where, L - Length observed by the observer L - Original length 0 v - Relative speed between the observer and object c - Speed of light Step 1: In this problem, we have to find out the length of the metre scale observed by the observer. So, the actual length of the metre scale is, 0 = 1 metre Velocity with which it travels = 99.5 % of c It is nothing but the relative speed between the observer and object. So, v = 99.5% c = (99.5 / 100) c = 0.995 c m/s Applying all these values in the equation for length contraction we get, (0.995 c) L = 1 metre × 1 c2 0.995 × c L = 1 metre × 1 c “c ” term on numerator and denominator will cancel each other. 0.995 = 0.990025 Putting this value in the equation we get, L = 1 metre × 1 0.990025 L = 1 metre × 0.009975 0.009975 = 0.099875 Therefore, L = 1 metre × 0.099875 = 0.099875 metres Conclusion: The length of the metre stick will be appeared as 0.099875 metres. If we convert this into centimetres, 1 m = 100 cm 0.099875 m = 0.099875 × 100 cm = 9.9875 cm 10 cm