The string of a simple pendulum is replaced by a uniform rod of length L and mass M while the bob has a mass m. It is allowed to make small oscillations. Its time period is

When the rod is replaced by the string the simple pendulum will act as compound pendulum for which time period is given byT=2πI0Mgd  ………(i)I0= moment of inertia about point of suspension=ML23+mL2=(M+3m)L23M' = total mass = (M + m)d = separation between point of suspension and centre of mass of the pendulum=M(L/2)+m(L)(M+m)=(M+2m)L2(M+m)Substituting the values in Eq. (i), we get⇒ T=2π2(M+3m)L3(M+2m)g