Answer
$1.50 \mathrm{s}$
Work Step by Step
$$T=2 \pi \sqrt{\frac{I}{(M+m) g d}}=2 \pi \sqrt{\frac{0.205 \mathrm{kg} \cdot \mathrm{m}^{2}}{(0.500 \mathrm{kg}+0.270 \mathrm{kg})\left(9.80 \mathrm{m} / \mathrm{s}^{2}\right)(0.447 \mathrm{m})}}=1.50 \mathrm{s}$$
