A) 1400 m
B) 2800 m
C) 700 m
D) 350 m
Correct Answer: A
Solution :
From the formula the induced emf due to electromagnetic inductions produced in a coil is given by \[{{E}_{0}}=nA\,B\omega \] (here \[n\] is the number of turns and \[\omega =2\pi f\] and A is area.) Given: \[{{n}_{1}}:{{n}_{2}}=50:100=1:2\] \[{{f}_{1}}:{{f}_{2}}=50:150=1:3\] Therefore the ratio of induced emf is \[\frac{{{\varepsilon }_{01}}}{{{\varepsilon }_{02}}}=\frac{{{n}_{1}}AB\,2\pi {{f}_{1}}}{{{n}_{2}}AB\,2\pi {{f}_{2}}}=\frac{1}{2}\times \frac{1}{3}=\frac{1}{6}\] The ratio will be \[{{\varepsilon }_{01}}:{{\varepsilon }_{02}}=1:6\]
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