Question

A 2.05-m-long rod, as measured in its rest frame, speeds by you longitudinally at 6.01 x 107 m/s. You measure its length as it passes. By how many millimeters do you determine the rod has contracted?

Answer 1

40 mm

Step-by-step explanation:

`L_o`=Proper Length of rod = 2.05 m

Speed of rod = 6.01×10⁷ m/s

Length contraction

`L=\sqrt{1-(v^2)/(c^2)}L_o\\\Rightarrow L=\sqrt{1-((6.01* 10^7)^2)/((3* 10^8)^2)}* 2.05=2.00844`

Final Length will be 2.01 m

So length that is contracted is 2.05-2.01 = 0.04 m

The length is contracted by 40 mm.