Properties of Solids & Fluids · JEE Advanced previous year questions

2024 2 questions

1. Q232024 · 26 May 2024 · Paper 2· One or more correct

   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 $500/9$.
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   Answer: A, B, D

2. Q302024 · 26 May 2024 · Paper 2· Numerical answer

   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 ____.

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   Answer: 96