Step 1: The angular momentum \( L \) of a particle rotating with respect to a central force is given by: \[ L = r \times p, \] where \( r \) is the position vector, and \( p \) is the linear momentum of the particle.
Step 2: The rate of change of angular momentum is related to the torque \( \tau \) acting on the particle: \[ \frac{dL}{dt} = \tau. \]
Step 3: If the torque \( \tau \) is zero, then the angular momentum remains constant. This happens when there is no external torque acting on the particle.
Step 4: Since central forces always act along the line joining the particle and the center of rotation, they produce zero torque. Therefore, the angular momentum of the particle remains constant.
Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.