GATE 1993 Mechanical Engineering (ME) Question Paper with Answer Key PDF

GATE Questions

• 1.

  A vibrating system has a critical damping coefficient \(C_c = 350 \, \text{N}\cdot\text{s/m}\) and an actual damping coefficient \(C = 35 \, \text{N}\cdot\text{s/m}\). The logarithmic decrement of the system is approximately:

  • 0.10
    
  • 0.31
    
  • 0.63
    
  • 3.14
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• 2.

  For the differential equation given below, which one of the following options is correct? \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0, \quad 0 \leq x \leq 1, 0 \leq y \leq 1 \]

  • \( u = e^{x + y} \) is a solution for all \(x\) and \(y\)
    
  • \( u = e^{x} \sin y \) is a solution for all \(x\) and \(y\)
    
  • \( u = \sin x \sin y \) is a solution for all \(x\) and \(y\)
    
  • \( u = \cos x \cos y \) is a solution for all \(x\) and \(y\)
    
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• 3.

  The welding process commonly used for fabricating tailor-welded blanks of dissimilar thickness for automotive applications is

  • arc welding
    
  • laser welding
    
  • gas welding
    
  • friction welding
    
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• 4.

  Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

  • \( (AB)^T = B^T A^T \)
    
  • \( AB = BA \)
    
  • \( A^T = A^{-1} \)
    
  • \( A = A^{-1} \)
    
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• 5.

  A cantilever beam of length \(L\) is fixed at the left end (\(x=0\)). It is subjected to a concentrated downward point load \(P\) and a concentrated clockwise moment \(M = \frac{PL}{2}\) at the midpoint (\(x = L/2\)). Which of the following descriptions correctly represents the Shear Force Diagram (SFD) for the beam?

  • A rectangular block of constant positive height \(P\) from \(x=0\) to \(x=L/2\), and zero shear force from \(x=L/2\) to \(x=L\).
    
  • A rectangular block of constant positive height \(P\) from \(x=0\) to \(x=L/2\), followed by another rectangular block of height \(P/2\) from \(x=L/2\) to \(x=L\).
    
  • A triangular shape increasing linearly from \(x=0\) to \(x=L/2\).
    
  • A rectangular block from \(x=0\) to \(x=L\), unaffected by the point load.
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• 6.

  Consider two infinitely long fins made of the same material and exposed to the same convective environment. One fin has a square cross-section of side \(a\), and the other has a circular cross-section of diameter \(d\). Assume \(a = d\). The ratio of the steady-state heat transfer rate from the square fin to that from the circular fin, \(\frac{\dot{Q}_{\text{square}}}{\dot{Q}_{\text{circular}}}\), is:

  • \(\frac{\pi}{4}\)
    
  • \(\frac{4}{\pi}\)
    
  • \(\frac{2}{\sqrt{\pi}}\)
    
  • \(\frac{\sqrt{\pi}}{2}\)
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