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Chapter 11 Properties of Matter and Fluids Previous Year Questions with Solutions

Pravegaa PYQ Series · Volume 2: Classical Mechanics & Special Relativity

CM11: Properties of Matter and Fluids

19 previous-year questions with complete solutions, from IIT JAM, GATE, CSIR NET-JRF, JEST and TIFR, arranged from IIT JAM and GATE through to TIFR and from the most recent paper backwards. Click Show solution under any question.

  • IIT JAM: 8
  • CSIR NET: 3
  • JEST: 2
  • TIFR GS: 6
CM11.1IIT JAM 2024, Q24MCQ | 2 marks

A tank, placed on the ground, is filled with water up to a height \(h\). A small hole is made at a height \(h_1\) such that \(h_1<h\). The water jet emerging from the hole strikes the ground at a horizontal distance \(D\), as shown schematically in the figure. Which of the following statements is correct?Figure(\(g\) is the acceleration due to gravity)

  1. Velocity at \(h_1\) IS \(\sqrt{2gh_1}\)

  2. \(D=2(h-h_1)\)

  3. \(D\) Will be maximum when \(h_1=\frac23h\)

  4. The maximum value of \(D\) is \(h\)

Show solution

By Torricelli's theorem the efflux speed depends on the depth of the hole below the free surface: \[ v=\sqrt{2g(h-h_1)} . \] Time of fall from height \(h_1\): \(t=\sqrt{2h_1/g}\). Range: \[ D=vt=2\sqrt{h_1(h-h_1)} . \] \(\dfrac{d}{dh_1}\left[h_1(h-h_1)\right]=h-2h_1=0\Rightarrow h_1=\dfrac h2\), giving \[ D_{\max}=2\sqrt{\frac h2\cdot\frac h2}=\boxed{h} \] So (A), (B), (C) are false and (D) is true.

Answer: (D) \(D_{\max}=h\)

CM11.2IIT JAM 2024, Q25MCQ | 2 marks

An incompressible fluid is flowing through a vertical pipe (height \(h\) and crosssectional area \(A_o\)). A thin mesh, having \(n\) circular holes of area \(A_h\), is fixed at the bottom end of the pipe. The speed of the fluid entering the top-end of the pipe is \(v_o\). The volume flow rate from an individual hole of the mesh is given by:

(\(g\) is the acceleration due to gravity)

  1. \(\dfrac{A_o}{n}\sqrt{v_o^2+2gh}\)

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