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NEET Sample Paper NEET Sample Test Paper-75

  • question_answer
    A wire x has a resistance of\[20\,\Omega \]. Another wire y of same material but length twice that of x resistance of \[8\,\Omega \]. If r is the radius of cross-section of x, then radius of cross-section of y is                                  

    A)  r                                 

    B)  \[\frac{r}{\sqrt{2}}\]

    C)  \[\sqrt{5}\,r\]                

    D)  2r

    Correct Answer: C

    Solution :

    As resistance, \[R=\frac{\rho l}{A}\] For wire x,    \[20=\frac{\rho l}{\pi {{r}^{2}}}\]                          ... (i) Similarly, for wire y, \[8=\frac{\rho (2l)}{\pi {{(r'\,)}^{2}}}\] Dividing Eq. (i) by (ii), we have \[\frac{20}{8}=\frac{\rho l}{\pi {{r}^{2}}}\times \frac{\pi {{(r\,'\,)}^{2}}}{\rho \,(20)}\] \[5={{\left( \frac{r'}{r} \right)}^{2}}\,\,\,\Rightarrow \,\,\,r'=\sqrt{5}\,\,r\]


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