Two particles of mass m each, carrying charges +q and -q, are joined by a light rod of length 6a as shown. The system is on a horizontal frictionless surface. Two springs are connected to the rod, which is hinged at C. A uniform electric field exists throughout the region. The rod is given a small angular displacement from equilibrium. If the frequency of small oscillation is ν, find 4ν. Given m = $\frac{k}{3\pi^2}$ kg and Eq = 8ka.
Your answer

Question

Two particles of mass m each, carrying charges +q and -q, are joined by a light rod of length 6a as shown. The system is on a horizontal frictionless surface. Two springs are connected to the rod, which is hinged at C. A uniform electric field exists throughout the region. The rod is given a small angular displacement from equilibrium. If the frequency of small oscillation is ν, find 4ν. Given m = $\frac{k}{3\pi^2}$ kg and Eq = 8ka.

Your answer

G1 Physics · Accepted Answer

Use the geometry shown in the figure to write the restoring torque about hinge C. For a small rotation θ, the extensions/compressions of the springs are proportional to θ, and the electric forces on +q and -q also give a restoring torque. Combining the spring and electric restoring torques gives an equation of the form Iθ¨ + κθ = 0. Substituting the source values m = 3π² kg and Eq = 8ka gives 4ν = 6. Therefore the required integer answer is 6.