NEET-XII-Physics
47: The Special Theory of Relativity
- #5A rod of rest length L moves at a relativistic speed. Let L‘ = L/γ. Its length
(a) must be equal to L‘
(b) may be equal to L
(c) may be more than L‘ but less than L
(d) may be more than LdigAnsr: b,cAns : (b) may be equal to L
(c) may be more than L' but less than L
If a rod of rest length L is moving at a relativistic speed v and its length is contracted to L', then
`` L\text{'}=\frac{L}{\gamma }=L\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}``
`` \,\mathrm{\,If\,}\gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}},\,\mathrm{\,then\,}v<<c,\gamma \cong 1.``
`` ``
`` \Rightarrow L\text{'}\cong L``
But the length of the rod may be more than L' depending on the frame of the observer. However, it cannot be more than L because as the speed of the rod increases, its length contracts more and more due to increasing value of `` \gamma ``.
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