Assume that a ship has length \(L = 200 \, \text{m}\) and operates at a design speed \(U = 12 \, \text{m/s}\). If in a turning circle maneuver the ship exhibits a steady turning diameter of \(6L\), then the yaw rate of the ship is ________________ rad/s (correct to two decimal places).
Show Hint
Correct Answer: 0.02
Solution and Explanation
Final Answer: 0.02–0.02 rad/s
Top Questions on Ship Dynamics
A ship of 3300 tonne displacement is undergoing an inclining experiment in seawater of density 1025 kg/m\(^3\). A mass of 6 tonne is displaced transversely by 12 m as shown in the figure. This results in a 0.12 m deflection of a 11 m long pendulum suspended from the centerline. The transverse metacenter of the ship is located at 7.25 m above the keel.
The distance of the center of gravity from the keel is ________ m (rounded off to two decimal places).
A multi-cell midship section of a ship with \( B = 40 \, {m} \) and \( D = 20 \, {m} \) is shown in the figure. The shear-flows are given as \( q_1 = q_2 = q_3 = 0.9376 \, {MN/m} \). The applied twisting moment on the midship section is ___________ MN·m (rounded off to two decimal places).
Consider a case where the load \( Q \) for a ship structure has only statistical uncertainties. The probability density function of the load \( p_Q(x) \) is shown in the figure. The characteristic limit value of the load \( Q_L \) is 1.5 and the factor of safety is 1. Which of the following probability of exceedance value(s) of the load will lead to a safe design?
- 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).
- 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?
Questions Asked in GATE NM exam
- If \( P e^x = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?
Bird : Nest :: Bee : __________
Select the correct option to complete the analogy.- Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
- GATE NM - 2025
- Continuity and differentiability
A closed system is undergoing a reversible process 1–P–2 from state 1 to 2, as shown in the figure, where X and Y are thermodynamic properties. An irreversible process 2–Q–1 brings the system back from 2 to 1. The net change in entropy of the system and surroundings during the above-mentioned cycle are _______ respectively.
- GATE NM - 2025
- Thermodynamics
Consider a weightless, frictionless piston with a 2 kg mass placed on it as shown in the figure. At equilibrium in position 1, the cylinder contains 0.1 kg of air. The piston cross-sectional area is 0.01 m2. The ambient pressure in the surroundings outside the piston-cylinder arrangement is 0 bar (absolute). When the mass above the piston is removed instantaneously, it moves up and hits the stop at position 2, which is 0.1 m above the initial position.
Assuming \( g = 9.81 \, {m/s}^2 \), the thermodynamic work done by the system during this process is ________ J (answer in integer).
- GATE NM - 2025
- Thermodynamics