NEET-XII-Physics
47: The Special Theory of Relativity
- #2-athe traveller and (b) a ground observer.Ans : The observer in the train notices the same values of l, b and h because the suitcase is in rest w.r.t. the traveller. (b) Since the suitcase is moving with a speed of 0.6c w.r.t. the ground observer, the component of length parallel to the velocity undergoes contraction, but the perpendicular components (breadth and height) remain the same.
So, the length that is parallel to the velocity of the train changes, while the breadth and height remain the same.
`` l\text{'}=l\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}``
`` =50\sqrt{1-\frac{{\left(0.6c\right)}^{2}}{{c}^{2}}}``
`` =50\sqrt{1-0.36}``
`` =50\sqrt{0.64}``
`` =50\times 0.8=40\,\mathrm{\,cm\,}``
Thus, the dimensions measured by the ground observer are 40 cm × 25 cm × 10 cm.
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- #2-ba ground observer.Ans : Since the suitcase is moving with a speed of 0.6c w.r.t. the ground observer, the component of length parallel to the velocity undergoes contraction, but the perpendicular components (breadth and height) remain the same.
So, the length that is parallel to the velocity of the train changes, while the breadth and height remain the same.
`` l\text{'}=l\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}``
`` =50\sqrt{1-\frac{{\left(0.6c\right)}^{2}}{{c}^{2}}}``
`` =50\sqrt{1-0.36}``
`` =50\sqrt{0.64}``
`` =50\times 0.8=40\,\mathrm{\,cm\,}``
Thus, the dimensions measured by the ground observer are 40 cm × 25 cm × 10 cm.
Page No 458: