To solve this problem, we need to understand the working principle of a transformer, specifically a step-up transformer. A transformer is a device used to increase or decrease the voltage of an alternating current (AC). It operates on the principle of electromagnetic induction and requires an AC input to function properly.
This particular problem involves a step-up transformer with a turn ratio of \(10:1\). The turn ratio indicates that the secondary winding has 10 times more turns than the primary winding. Therefore, if an AC voltage is applied to the primary, the secondary voltage will be increased by a factor of 10.
However, the critical point here is that the source provided to the primary is a cell with an electromotive force (emf) of \(2\,V\). Cells provide direct current (DC), and transformers do not work with DC voltages because a steady current does not create a changing magnetic field, which is necessary for induction in the secondary winding.
Given that the input is a DC voltage, the transformer will not be able to operate, and thus no voltage will be developed in the secondary winding. Therefore, the secondary voltage developed is zero.
Conclusion: The correct answer is zero, as transformers require AC to work, and a DC input results in no induced voltage in the secondary.