a
(a)

Time period \(=2 \pi \sqrt{\frac{1}{g}}\)

\(T \propto \sqrt{I}\)

\(\frac{T^{\prime}}{T} \propto \sqrt{\frac{I^{\prime}}{I}}\)

\(T=T \sqrt{\frac{1+l \propto \Delta \theta}{I}}\)

\(T=T\left(1+\frac{1}{2} \propto \Delta \theta\right)[\alpha \Delta \theta=0.002]\)

\(\Delta T=T-T=\frac{1}{2} T \propto \Delta \theta=T \times 0.001\)

Time lost in time \(t\) is

\(\Delta T=\frac{1}{2} \quad t=1 \text { day }=24 \times 3600 \,s =86400 \,s\)

\(\Delta T=\left(\frac{\Delta T}{T}\right) \times t\)

\(\Delta T=0.001 \times 86400\)

\(\Delta T=86.4 \,s\)