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NEET-XII-Physics

47: The Special Theory of Relativity

with Solutions - page 2
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  • #3
    The length of a rod is exactly 1 m when measured at rest. What will be its length when it moves at a speed of (a) 3 × 105 m s-1, (b) 3 × 106 m s-1 and (c) 3 × 107 m s-1?
    Ans : Given:
    Proper length of the rod, L = 1 m
    If v is the velocity of the rod, then the moving length of the rod is given by
    `` L\text{'}=L\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}`` (a) Here,
    v = 3 × 105 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{10}}{9\times {10}^{16}}}``
    `` =\sqrt{1-{10}^{-6}}=0.9999995\,\mathrm{\,m\,}`` (b) Here,
    v = 3 × 106 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{12}}{9\times {10}^{16}}}``
    `` =\sqrt{1-{10}^{-4}}``
    `` =0.99995\,\mathrm{\,m\,}`` (c) Here,
    v = 3 × 107 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{14}}{9\times {10}^{16}}}``
    `` =1\sqrt{1-{10}^{-2}}``
    `` =0.995\,\mathrm{\,m\,}``
    Page No 458:
  • #3-a
    3 × 105 m s-1,
    Ans : Here,
    v = 3 × 105 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{10}}{9\times {10}^{16}}}``
    `` =\sqrt{1-{10}^{-6}}=0.9999995\,\mathrm{\,m\,}``
  • #3-b
    3 × 106 m s-1 and
    Ans : Here,
    v = 3 × 106 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{12}}{9\times {10}^{16}}}``
    `` =\sqrt{1-{10}^{-4}}``
    `` =0.99995\,\mathrm{\,m\,}``
  • #3-c
    3 × 107 m s-1?
    Ans : Here,
    v = 3 × 107 m/s
    `` L\text{'}=1\times \sqrt{1-\frac{9\times {10}^{14}}{9\times {10}^{16}}}``
    `` =1\sqrt{1-{10}^{-2}}``
    `` =0.995\,\mathrm{\,m\,}``
    Page No 458: