solid angle subtended by ring is 2π(1−cosθ)...(i)
given the flux through the disc is 1/4th of total flux, the solid angle subtended by disc will be 1/4th of total solid angle which is 144π=πfrom equation (i)
2π(1−cosθ)=π⇒cosθ=12 from geometry cosθ=a√a2+R2=12
⇒a=R√3
hence correct answer is 3.