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 $25.0 \mathrm{~cm}$ and a moment of inertia of $1 / 2 \mathrm{MR}^{2}$ . If $\mathrm{m}_{1}$ is $1.00 \mathrm{~kg}, \mathrm{~m}_{2}$ is $2.00 \mathrm{~kg}$ , and M is $4.00 \mathrm{~kg}$ , then what is the downward acceleration of $m_{1}$ ?

A) $2.72 \mathrm{~m} / \mathrm{s}^{2}$
B) $1.55 \mathrm{~m} / \mathrm{s}^{2}$
C) $1.96 \mathrm{~m} / \mathrm{s}^{2}$
D) $2.06 \mathrm{~m} / \mathrm{s}^{2}$
E) $2.33 \mathrm{~m} / \mathrm{s}^{2}$