Answer :
To solve the problem it is necessary to apply all the concepts related to the definition of Torque, both linear and angular.
From the linear definition the torque is defined as
[tex]\tau = F*r[/tex]
Where,
F = Force
r = radius
On the other hand we have that,
[tex]\tau = I \alpha[/tex]
Where,
I = Moment of inertia
[tex]\alpha =[/tex] Angular Acceleration
Using the first equation we can find the Torque, there,
[tex]\tau = F*r[/tex]
[tex]\tau = (2*10^3)(0.05)[/tex]
[tex]\tau = 100Nm[/tex]
Therefore the Inertia moment can be calculated from the second equation,
[tex]\tau = I \alpha[/tex]
[tex]I = \frac{\tau}{\alpha}[/tex]
[tex]I = \frac{100}{125}[/tex]
[tex]I = 0.8 kg.m^2[/tex]
Therefore the value of moment of inertia is [tex]0.8 Kg.m^2[/tex]