What will happen to the transformer if rated voltage is applied to the winding during short circuit test?

If rated voltage is applied to Transformer during S/C test, The secondary winding will burn out due ta heavy current flow through the winding. During S/C test the secondary winding is short circuited so the impedance between phase and neutral is very low(only winding resistance). But the voltage across the secondary winding is rated hence heavy current flows through the winding, as I=V/Z.

it depends which rated voltage is applied. if you are talking about primary winding voltage, transformer should withstand the primary rated voltage it's been designed for (OR it has been poorly designed). Otherwise, if rated voltage is the insulation voltage between a winding and earth OR winding-to-winding, you just have to check if: 1 - it is higher than the maximum primary winding voltage the transformer can withstand (could be, could not be..). Then, you can guess if your transformer is likely to burn or not. 2 - your test setup (usually a HV generator connected between primary and secondary winding) can deliver the requested current for the setup. I guess this won't be the case, since HV testers are usually designed to generate high voltages, but very small output currents.