b
From, the, relation
\(h = ut = \frac{1}{2}g{t^2}\)
\(h = \frac{1}{2}g{t^2}\)\( \Rightarrow g = \frac{{2h}}{{{t^2}}}\) (body, initially, at, rest)

Taking, natural, log aritham, on, both, sides, we, get

\(In\,g = In\,h - 2\,In\,t\)

Differentiating, \(\frac{{\Delta h}}{g} = \frac{{\Delta h}}{h}\, - 2\,\frac{{\Delta t}}{t}\)
For, max imum, permissible, error,

or,\({\left( {\frac{{\Delta g}}{g} \times 100} \right)_{\max }} = \left( {\frac{{\Delta h}}{h} \times 100} \right) + 2 \times \left( {\frac{{\Delta t}}{t} \times 100} \right)\)

According, to, problem

\(\frac{{\Delta h}}{h} \times 100{ = _{{e_1}}}\,and\,\frac{{\Delta t}}{t} \times 100{ = _{{e_2}}}\)

Therefore, \(( {\frac{{\Delta g}}{g} \times 100} )_{\max } = {e_1} + 2{e_2}\)