Please Explain your answer. Why isnt the Vrms = Vpeak/ root 2 when the diode has negligible resistance

Dear student,

AC source has direction of voltage reversing periodically. Diode allows current to flow through itself only in one direction and stops the other. Henc the AC voltage appearing across the resistor for the time when AC source give voltage in opposite direction is zero as shown in the figure.

Hence, in total, the time for which the voltage appears over resitsor is also halved, and so is the rms value of it.