Question

calculate the percentage contraction of a rod moving with a velocity of 0.8c in a direction inclined at 60° to its own length​

Answer 1

Answer:

Let lo be the length of the rod in the frame in which it is at rest and s' is the frame which is moving with a speed 0.8c in a direction making an angle 60° with x-axis. The components of lo along and perpendicular to the direction of motion are lo cos 60° and lo sin 60° respectively.

Now length of the rod along the direction of motion

= lo cos 60°_/1-(0.8) 2/c2

= lo/2×0.6

= 0.3 lo.

Length of the rod perpendicular to the direction of motion.

= lo sin 60°

=_/3/2 lo

Length of moving rod

l = [(0.3lo)2+{lo_/3/2} 2] 1/2

= 0.916 lo.

Percentage contraction

= lo-0.916lo/lo×100

= 8.4%.

Explanation:

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