CBSE-XI-Physics
47: The Special Theory of Relativity
- #15At what speed the volume of an object shrinks to half its rest value?Ans : Let the initial volume of the object be V and the speed of the object be v respectively.
According to the question, volume of the object shrinks to half of its rest value. So apparent volume is given by
`` V\text{'}=\frac{V}{2}``
`` \,\mathrm{\,Now\,},``
`` V\text{'}=V\sqrt{1-{v}^{2}/{c}^{2}}``
`` \Rightarrow \frac{V}{2}=V\sqrt{1-{v}^{2}/{c}^{2}}``
`` \Rightarrow \frac{c}{2}=\sqrt{{c}^{2}-{v}^{2}}``
`` \Rightarrow \frac{{c}^{2}}{4}={c}^{2}-{v}^{2}``
`` \Rightarrow {v}^{2}={c}^{2}-\frac{{c}^{2}}{4}=\frac{3}{4}{c}^{2}``
`` \Rightarrow v=\frac{\sqrt{3}}{2}c``
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