A semicircular  loop of radius r is being rotated about an axis normal to the plane of loop as shown such  that when loop is going inside the field $\mathrm{\omega }={\mathrm{\omega }}_0$ and when loop is coming out of the field $\mathrm{\omega }=2{\mathrm{\omega }}_0$ which of the following best represents the emf(e) induced as function of time with anticlockwise sense as +ve:

When loop enters into the magnetic field and magnetic flux through it increases;

$Area A=\left(\frac{\pi r^2}{2\pi }\right)\theta =\frac{\pi r}{2}\theta$

$Flux \varphi =BA$

$EMF e=\frac{d\varphi }{dt}=\frac{B\pi r}{2}\frac{d\theta }{dt}=\frac{B\pi r}{2}\omega$

Induced emf will be constant and anticlockwise upto $\mathrm{t}=\frac{\mathrm{T}}{2}=\frac{\mathrm{\pi }}{{\mathrm{\omega }}_0}$.
After this time, the loop comes out of the magnetic field and magnetic flux through it decreases; the induced current will be constant and clockwise upto time $\frac{\mathrm{\pi }}{{\mathrm{\omega }}_0}+\frac{\mathrm{\pi }}{2{\mathrm{\omega }}_0}=\frac{3}{2}\frac{\mathrm{\pi }}{{\mathrm{\omega }}_0}$.