A conducting rod of length \(L\) lies in \(X Y\)-plane and makes an angle \(30^{\circ}\) with \(X\)-axis. One end of the rod lies at origin initially. A magnetic field also exists in the region pointing along positive \(Z\)-direction. The magnitude of the magnetic field varies with \(y\) as \(B_0\left(\frac{y}{L}\right)^3\), where, \(B_0\) is a constant. At some instant the rod starts moving with a velocity \(v_0\) along \(X\)-axis. The emf induced in the rod is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.