The Time-keeper

the time period of a physical pendulum is given by $2\pi\sqrt{\frac{I}{mgd}}$ ---------------------- $\boxed{i}$

we will not go into how this is got. one can find the derivation in any good mechanics book.

now assuming that the reader knows the theorems of inertia(ie.,parallel axis theorem,perpendicular axis theorem,pappus theorem), i will claim that the moment of inertia of the composite system about axis of oscillation $O$ IS $\frac{34mR^{2}}{6}+2ml^{2}+6mlR$

$d$ is the distance of centre of mass from the point of oscillation $O$

this is easily computed to be $l+\frac{3R}{2}$

now substituting in $\boxed{i}$ ,

$T = 2\pi\sqrt{\frac{34R^{2}+12l^{2}+36lR}{6g(3R+2l)}}$

from here, T=3.31 seconds

thus,the man has counted 3 seconds