Final answer:
To find the tension in the string attached to mass m1 while considering a pulley of a given mass and moment of inertia, one needs to apply Newton's second law to both masses and the rotational dynamics equation to the pulley, which involves the linear acceleration of the masses and the angular acceleration of the pulley.
Step-by-step explanation:
The question involves calculating the tension in the string that is attached to mass m1 in a system involving two masses and a pulley with inertia.
The pulley has a mass m and a moment of inertia given by I = mr^2, where r is the radius. The tension in the string can be calculated by applying Newton's second law to each mass and using the rotational dynamics of the pulley.
Due to the fact that the pulley has mass and a given moment of inertia, it also has angular acceleration. Therefore, we can't simply treat this as a direct mass-to-mass comparison.
We first need to establish the relationship between the linear accelerations of the masses and the angular acceleration of the pulley, using a = αr, where a is the linear acceleration and α is the angular acceleration.
Next, we write down the equation of motion for each mass and the rotational equation of motion for the pulley to solve for the tension in the string attached to m1 and the acceleration of the system.
These equations will include the tension in the strings, gravity forces, and net torque on the pulley due to the tensions.
However, without the complete set of equations or a diagram, it is not possible to provide the exact numerical value for the tension in this question.
The student would need to use the provided masses, moment of inertia, and gravitational acceleration to find the acceleration and then solve for the tension considering the system of two masses and a pulley with inertia.