c
Time period of Oscillation, \(T=2 \pi \sqrt{\frac{1}{M B}}\)

\(\Rightarrow \frac{1}{4}=2 \pi \sqrt{\frac{9.8 \times 10^{-6}}{M \times 0.049}}\)

\(\Rightarrow \frac{1}{16}=4 \pi^2 \times \frac{9.8 \times 10^{-6}}{M \times 49 \times 10^{-3}}\)

\(\Rightarrow M=\frac{4 \pi^2 \times 9.8 \times 10^{-6}}{49 \times 10^{-3}} \times 16\)

\(\frac{4 \pi^2 \times 9.8 \times 16 \times 10^{-3}}{49}\)

\(\quad=12.8 \pi^2 \times 10^{-3} \times 10^{-2} \times 10^2\)

\(=1280 \pi^2 \times 10^{-5} \mathrm{Am}^2\)