A rod pivoted at one of its end undergoes simple harmonic motion when given a  small oscillation. If the pivot is changed such that its moment of inertia decreases  to half of its original value, then its new time period is

For angular oscillation  ω=cIHence T=2πIc …………(1)Since time period is directly proportional to root of moment of inertia, the new time  period is  T'=2πI2c…………(2)Using equation (1) and (2), it can be concluded that new time period is  T'=T2