Time period of Oscillation, $$T=2 \pi \sqrt{\frac{I}{M B}}$$

$$\begin{aligned} & \Rightarrow \frac{1}{4}=2 \pi \sqrt{\frac{9.8 \times 10^{-6}}{M \times 0.049}} \\ & \Rightarrow \quad \frac{1}{16}=4 \pi^2 \times \frac{9.8 \times 10^{-6}}{M \times 49 \times 10^{-3}} \\ & \Rightarrow \quad M=\frac{4 \pi^2 \times 9.8 \times 10^{-6}}{49 \times 10^{-3}} \times 16 \\ & \quad=\frac{4 \pi^2 \times 9.8 \times 16 \times 10^{-3}}{49} \\ & \quad=12.8 \pi^2 \times 10^{-3} \times 10^{-2} \times 10^2 \\ & =1280 \pi^2 \times 10^{-5} \mathrm{Am}^2 \end{aligned}$$