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QPage 458: Q2: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q2 Solution: A suitcase kept on a shop's rack is measured 50 cm _ 25 cm _ 10 …

A suitcase kept on a shop's rack is measured 50 cm _ 25 cm _ 10 cm by the shop's owner. A traveller takes this suitcase in train moving with velocity 0.6c. If the suitcase is placed with its length along the train's velocity, find the dimensions measured by a) the traveller and b) a ground observer.

Step-by-Step Verified Solution

**Answer:** (a) Traveller: 50×25×1050 \times 25 \times 10 cm. (b) Ground observer: 40×25×1040 \times 25 \times 10 cm. **Step-by-Step Explanation:** (a) The traveller is at rest relative to the suitcase, so he measures the proper dimensions: 50×25×1050 \times 25 \times 10 cm. (b) For the ground observer, the suitcase is moving at 0.6c0.6c along its length. Length contraction:
L=L01−0.62=50×0.64=50×0.8=40 cmL = L_0\sqrt{1 - 0.6^2} = 50 \times \sqrt{0.64} = 50 \times 0.8 = 40 \text{ cm}
The other dimensions (perpendicular to motion) are unchanged: 25 cm and 10 cm.

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