For a soap bubble, there are two liquid-air surfaces, so the excess pressure \( \Delta P \) inside the bubble is given by:
\[\Delta P = 2 \left( \frac{2S}{R} \right) = \frac{4S}{R}\]
Choose the correct set of reagents for the following conversion:
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):