2 questions
A spherical soap bubble inside an air chamber at pressure \( P_0 = 10^{5} \,\text{Pa} \) has a certain radius so that the excess pressure inside the bubble is \( \Delta P = 144 \,\text{Pa} \). Now, the chamber pressure is reduced to \( \frac{8 P_0}{27} \) so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure \( \Delta P \) in both the cases to be much smaller than the chamber pressure. The new excess pressure \( \Delta P \) in \( \text{Pa} \) is: ___.
A table tennis ball has radius \( \left(\frac{3}{2}\right)\times 10^{-2} \, \text{m} \) and mass \( \left(\frac{22}{7}\right)\times 10^{-3} \, \text{kg} \). It is slowly pushed down into a swimming pool to a depth of \( d = 0.7 \, \text{m} \) below the water surface and then released from rest. It emerges from the water surface at speed \( v \), without getting wet, and rises up to a height \( H \). Which of the following option(s) is(are) correct?
[given: \( \pi = \frac{22}{7} \), \( g = 10 \, \text{m s}^{-2} \), density of water \( = 1 \times 10^{3} \, \text{kg m}^{-3} \), viscosity of water \( = 1 \times 10^{3} \, \text{Pa−s} \).]
