1. A ring of mass \(m\) and radius \(R\) rolls without slipping on a horizontal surface with velocity \(v_0\). It encounters a frictionless inclined plane of angle \(\theta\). To what maximum vertical height \(h\) does the ring rise on the incline?
2. A circular loop of wire of radius \(R\) carries a current \(I\). A uniform magnetic field \(B\) is applied perpendicular to the plane of the loop. What is the tension induced in the wire of the loop?
3. A parallel plate capacitor with plate area \(A\) and separation \(d\) is filled with two dielectric slabs of thickness \(d/2\) having dielectric constants \(K_1\) and \(K_2\). What is the equivalent capacitance?
4. A particle of mass \(m\) moves under a central force field given by \(F(r) = -\frac{k}{r^3}\). For circular orbit of radius \(R\), what is its total mechanical energy?
5. In a Young's double slit experiment, one slit is covered by a thin glass plate of refractive index \(\mu\) and thickness \(t\). By how much distance does the central bright fringe shift on the screen (slit separation \(d\), screen distance \(D\))?