Final answer:
Using Newton's second law and the rotational motion equations, the acceleration of the suspended mass is calculated to be approximately 3.27 m/s^2, which is closest to answer option a) 3.5 m/s^2, although it is not an exact match.
Step-by-step explanation:
To calculate the acceleration of the suspended mass m using the given parameters of the uniform solid cylinder, we apply Newton's second law and the rotational equivalent of Newton's second law (torque = moment of inertia x angular acceleration) simultaneously.
First, the torque caused by the hanging mass m on the cylinder is Tau = m*g*R, where R is the radius of the cylinder, g is acceleration due to gravity, and m is the suspended mass. Using the given moment of inertia I = 1/2 * M * R2 for the cylinder, and knowing that torque is also equal to I*alpha (where alpha is the angular acceleration), we can write:
Tau = I*alpha = (1/2 * M * R2)*alpha
Therefore, m*g*R = (1/2 * M * R2)*alpha
After canceling R and rearranging the formula to solve for alpha, we get:
alpha = (2*m*g) / (M*R)
The linear acceleration a of the hanging mass is related to the angular acceleration alpha by a = alpha*R. Substituting the expression we obtained for alpha gives:
a = (2*m*g*R) / (M*R2) = (2*m*g) / (M*R)
Substituting the given values M = 1.5 kg, R = 0.08 m, m = 2 kg, and g = 9.8 m/s2, we find:
a = (2*2 kg*9.8 m/s2) / (1.5 kg*0.08 m)
a = (39.2 kg*m/s2) / (0.12 kg*m)
a = 326.666... m/s2
Upon calculating, we find that the acceleration 'a' is approximately 3.27 m/s2, which is not precisely any of the options given (a) 3.5 m/s2, (b) 2.5 m/s2, (c) 4.0 m/s2, (d) 5.0 m/s2. The closest answer to the calculated acceleration would be option (a) 3.5 m/s2, but please note that it is not exact.