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I studied that no body can travel with the velocity of light. But, assuming that when a body moves nearly velocity of light, will it obey length contraction law of Einstein or will it emit the same wavefront when it is in stationary state? What will happen to its dimensions? Will it appear same or shrink to an stationary observer?

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Since there are numerous questions under the tags and which can answer your question, I'll try to explain it precisely as possible.

no body can travel with the velocity of light

You're quite correct that no massive body can be accelerated to $c$, as it requires infinite energy.

assuming that when it moves nearly velocity of light, will it obey length contraction law of Einstein

This looks quite ridiculous to me. YES. That's why it's a widely accepted theory. It also agrees with experiments (like the decay of muons.). A short googling can answer that..! Even Wiki is far better.

What will happen to its dimensions? Will it appear same or shrink to an stationary observer?

It appears to be rotated. Have a look at this question:
What does a sphere moving close to the speed of light look like?

(How can it remain the same when space & time changes as we near $c$?)

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