List of top Questions asked in GATE NM

A square‑shaped body is subjected to only direct tensile stresses \(\sigma_x\) and \(\sigma_y\) as shown. If \(\sigma_x > \sigma_y\), then the value of normal stress (\(\sigma_{\theta}\)) and shear stress (\(\tau_{\theta}\)) respectively are ________.


 

The dynamics of a 90 m long ship are governed by the non-dimensional Nomoto equation. The magnitude of Nomoto gain \( |K'| = \frac{72}{35\pi} \) and that of Nomoto time constant \( |T'| = \frac{288}{35\pi} \). The steady turning radius of the ship for a 35° turning circle maneuver is ________ m (answer in integer).
Choose the correct statement(s) from the following with respect to a ship-generated Kelvin wave pattern in deep water.
Which of the following components is/are NOT found in a two-stroke marine diesel engine?
For a freely floating body in water, which of the following degrees of freedom has/have inherent restoring force?

The midship section of a barge of breadth \( W \) and depth \( H \) is shown in the figure. All plate thicknesses are equal. The barge is subjected to a longitudinal bending moment in the upright condition. Which one of the following statements is correct?


 

A ship of 5000 tonne displacement has two empty rectangular double bottom tanks with dimensions:
Tank A: length 12 m, width 16 m, and height 2 m
Tank B: length 16 m, width 12 m, and height 2 m
The length of each tank is oriented along the length of the ship. It is required to ballast the ship with 192 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
Which one of the following is the most common type of gear assembly used for coupling steam turbine and propeller shafts?
In ships, a flash evaporator is used to obtain ________.
In the stress-strain curve of mild steel, plastic deformation starts at the ________.
The dynamic response amplitude \( |H(\omega)| \) of a single degree of freedom system subjected to support motion is given by the following expression: \[ |H(\omega)| = \sqrt{\frac{1 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2 }{\left[ 1 - \left( \frac{\omega}{\omega_n} \right)^2 \right]^2 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2} } \] Where the damping ratio is \( \zeta \), the excitation frequency is \( \omega \), and the natural frequency of the system is \( \omega_n \). The amplitude \( |H(\omega)| \) increases with an increase in damping ratio (\( \zeta \)) if the excitation frequency (\( \omega \)) is ________ the natural frequency (\( \omega_n \)) of the system.
According to linear water wave theory, at a point on the free surface of a regular wave, the phase difference between the free surface elevation and the horizontal water particle acceleration is ________.
Which one of the following wave energy spectra is formulated for two peaks?
For marine engine shafts subjected to high radial and axial thrust loads, which one of the following types of bearings is the most suitable?
In a laminar boundary layer, the ratio of boundary layer thickness (\( \delta \)) to the corresponding displacement thickness (\( \delta^* \)) lies between ________.
The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is ________.
Identify the range of Reynolds number (Re) for a creeping flow.
The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the ________.
For all real values of \( x \) and \( y \), the partial differential equation in terms of \( \psi(x, y) \) given by \[ \frac{\partial^2 \psi}{\partial x^2} + 2 \frac{\partial^2 \psi}{\partial x \partial y} - 3 \frac{\partial^2 \psi}{\partial y^2} = 0 \] is ________
The Fourier series expansion of \( f(x) = \sin^2 x \) in the interval \((- \pi, \pi)\) is ______.
The value of \( \lim_{t \to 1} \frac{\ln t}{t^2 - 1} \) is ________.
A ship moving at a steady forward speed of \(10 \, {m/s}\) experiences a total resistance of \(140 \, {kN}\). The Quasi Propulsive Coefficient (QPC) is \(0.70\); the propeller shaft losses are \(5\%\) and the mechanical efficiency of the main engine is \(80\%\).
The indicated power of the main engine is ________ kW (rounded off to two decimal places).
A single degree of freedom system is undergoing free oscillation. The natural frequency and damping ratio of the system are \(1 \, {rad/sec}\) and \(0.01\) respectively.
The reduction in peak amplitude over three cycles is ________ % (rounded off to one decimal place).
A two-stroke four-cylinder large marine diesel engine has a cylinder bore of \(600 \, {mm}\) and stroke length of \(2400 \, {mm}\). The brake thermal efficiency (\( \eta_{{bth}} \)) is 45%, and fuel consumption rate (\( \dot{m}_f \)) is \(0.265 \, {kg/s}\) at an engine speed (\( N \)) of 100 rpm. Assuming the calorific value of fuel is \(42 \, {MJ/kg}\), the brake mean effective pressure (bmep) is ________ bar (rounded off to one decimal place).
The value of \( \int_1^3 \int_2^5 x^2 y \, dx \, dy \) is ________(answer in integer).