A Mass $m_{1}$ Is Connected by a Light String That Passes Over a Passes

Multiple Choice

A mass $m_{1}$ is connected by a light string that passes over a pulley of mass $M$ to a mass $m_{2}$ sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of $25 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$ . If $\mathrm{m}_{1}$ is $4.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $2.00 \mathrm{~kg}$ , and $\mathrm{M}$ is $4.00 \mathrm{~kg}$ , then what is the downward acceleration of $\mathrm{m}_{1}$ ?

A) $4.9 \mathrm{~m} / \mathrm{s}^{2}$
B) $4.5 \mathrm{~m} / \mathrm{s}^{2}$
C) $3.7 \mathrm{~m} / \mathrm{s}^{2}$
D) $4.1 \mathrm{~m} / \mathrm{s}^{2}$
E) $3.9 \mathrm{~m} / \mathrm{s}^{2}$