XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is l. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L>l) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is ______ m/s. (g= acceleration due to gravity)
(A)B2l22mgR
(B)B2l28mgR
(C)B2L22mgR
(D)B2l2mgR✓ Correct
Answer: (D)
Solution
As the rod falls with speed v, only the length l between the rails lies in the circuit, so the induced emf is ε=Bvl and the current is i=RBvl. The magnetic force on the rod, F=Bil=RB2l2v, acts upward and grows with v. At the terminal speed this balances gravity, mg=RB2l2vt, so vt=B2l2mgR.
JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option