Two metallic rings A and B, identical in shape and size but having different resistivities $$\rho_A$$ and $$\rho_B$$, are kept on top of two identical solenoids as shown in the figure below. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights $$h_A$$ and $$h_B$$, respectively, with $$h_A > h_B$$. The possible relation(s) between their resistivities and their masses $$m_A$$ and $$m_B$$ is (are)
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,
A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,
Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II:
| Column I | Column II | ||
|---|---|---|---|
| (A) | The energy of the system is increased. | (P) | System : A capacitor, initially uncharged. Process : It is connected to a battery. |
| (B) | Mechanical energy is provided to the system, which is converted into energy of random motion of its parts. | (Q) | System : A gas in an adiabatic container filled with an adiabatic piston. Process : The gas is compressed by pushing the piston. |
| (C) | Internal energy of the system is converted into its mechanical energy. | (R) | System : A gas in a rigid container. Process : The gas gets cooled due to colder atmosphere surrounding it. |
| (D) | Mass of the system is decreased. | (S) | System : A heavy nucleus, initially at rest. Process : The nucleus fissions into two fragments of nearly equal masses and some neutrons are emitted. |
| (T) | System : A resistive wire loop. Process : The loop is placed in a time varying magnetic field perpendicular to its plane. |