\(m =100 \,g =0.1 \,kg\)

\(\vec{a}=\frac{\overrightarrow{ F }}{ m }=100 \hat{ i }+50 \hat{ j }\)

\(\overrightarrow{ S }=\overrightarrow{ u t}+\frac{1}{2} \overrightarrow{ a }{ }^{2}=\frac{1}{2} \overrightarrow{ a } t ^{2}(\) as \(\overrightarrow{ u }=0)\)

\(=\frac{1}{2}(100 \hat{ i }+50 \hat{ j }) 2^{2}\)

\(=200 \hat{i}+100 \hat{j}\)

\(=a \hat{i}+b \hat{j}\)

\(a=200, b=100\)

\(\therefore \frac{a}{b}=2\)