GATE Electrical Engineering (EE) 2018 Solved Paper

Given, separately initiated DC motor.
Field excitation is constant.Producing a torque of $500\mathit{N}-\mathit{m}$
At zero speed,

and ${\mathit{E}}_{\mathit{b}}={\mathit{V}}_{\mathit{t}}-{\mathit{I}}_{\mathit{a}}{\mathit{r}}_{\mathit{a}}$
${\mathit{I}}_{\mathit{a}}=\frac{{\mathit{V}}_{\mathit{t}}}{{\mathit{r}}_{\mathit{a}}}=\frac{100}{0.05}=2000\mathit{A}$
Since $\mathit{T}={\mathit{K}}_{\mathit{a}}\mathit{\varnothing }{\mathit{I}}_{\mathit{a}}$
${\mathit{K}}_{\mathit{a}}\mathit{\varnothing }=\frac{500}{2000}=\frac{1}{4}$
When motor runs on no-load given all mechanical losses neglected. No-load current is negligible and the voltage drop at no-load can be negligible.
$\mathit{S}\mathit{o},{\mathit{E}}_{\mathit{b}}={\mathit{V}}_{\mathit{t}}=150\mathit{V}$
${\mathit{E}}_{\mathit{b}}={\mathit{K}}_{\mathit{a}}\mathit{\varnothing }{\mathit{\omega }}_{\mathit{m}}$
${\mathit{\omega }}_{\mathit{m}}=\frac{150}{\frac{1}{4}}$
${\mathit{\omega }}_{\mathit{m}}=150\times 4=600\mathit{r}\mathit{a}\mathit{d}∕\mathit{s}$