Answer
a) 305.5 N
b) 165 kilograms
Work Step by Step
a) We use Newton's Second Law to find:
$T = mg - ma = (50)(9.81-3.7)=305.5 \ N$
b) We use the equation for torque to find rotational inertia:
$I =\frac{\tau}{\alpha} \\ I= \frac{Fr}{\frac{a}{r}}$
$\frac{1}{2}mr^2 =\frac{Fr^2}{a}\\ m = \frac{2F}{a}=\frac{2\times 305.5}{3.7}=165.135\ kg$
