A charged mass m on a smooth inclined plane is attached to spring of constant K. Uniform magnetic field B lies parallel to plane, perpendicular to spring. Student expresses period as T = 2π√(m(1 + q²B²/mK)/K) in parameterized form; find requested coefficient combination according to the source. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A charged mass m on a smooth inclined plane is attached to spring of constant K. Uniform magnetic field B lies parallel to plane, perpendicular to spring. Student expresses period as T = 2π√(m(1 + q²B²/mK)/K) in parameterized form; find requested coefficient combination according to the source. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Magnetic Lorentz force qv⃗ ×B⃗ acts perpendicular to v⃗ and B⃗, so it does zero work. Step 2 — For B⃗ parallel to incline but perpendicular to spring and velocity along incline, magnetic force is normal to the surface, changing the normal reaction only. Step 3 — Along the incline, the linear restoring force is still F = −Kx; gravity contributes only an equilibrium shift. Step 4 — Angular frequency ω = √(K/m), time period T = 2π√(m/K). Thus no magnetic correction is needed, agreeing wit…