Properties of Solids & Fluids · JEE Advanced previous year questions

A table tennis ball has radius $(3/2)\times 10^{-2}\mathrm{m}$ and mass $(22/7)\times 10^{-3}\mathrm{kg}$. It is slowly pushed down into a swimming pool to a depth of $d=0.7\mathrm{m}$ 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: $\pi =22/7$, $g=10\mathrm{m}{\mathrm{s}}^{-2}$, density of water $=1\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$, viscosity of water $=1\times 10^{-3}\mathrm{Pa}\text{-}\mathrm{s}$.]

1. A.The work done in pushing the ball to the depth $d$ is $0.077\mathrm{J}$.
2. B.If we neglect the viscous force in water, then the speed $v=7m/s$.
3. C.If we neglect the viscous force in water, then the height $H=1.4\mathrm{m}$.
4. D.The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is $500/9$.

A spherical soap bubble inside an air chamber at pressure $P_0=10^5\mathrm{Pa}$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144\mathrm{Pa}$. Now, the chamber pressure is reduced to $8P_0/27$ 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 Pa is ____.