11
The meatcentric height of a ship is 0.6 m and the radius of gyration is 4 m. The time of rolling of a ship is
Answer & Solution
Answer: Option
C
Solution:
First, we need to understand what the question is asking. It wants us to calculate the time it takes for the ship to roll from one side to the other and back again.
Here's the formula we'll use: T = 2π * √(k² / (g * GM))
Where:
T is the time of rolling (what we want to find).
k is the radius of gyration (given as 4 m). This tells us how the ship's mass is distributed around its center of rotation. A larger radius means more resistance to rolling.
g is the acceleration due to gravity (approximately 9.81 m/s²). This is a constant.
GM is the metacentric height (given as 0.6 m). This is a measure of the ship's initial stability. A larger GM means the ship is more stable (resists rolling more), but can also mean a quicker, more uncomfortable roll. A smaller GM means less initial stability, potentially leading to capsizing if too small.
Now, let's plug in the values:
T = 2 * π * √(4² / (9.81 * 0.6))
T = 2 * π * √(16 / 5.886)
T = 2 * π * √2.718
T = 2 * π * 1.649
T ≈ 10.36 seconds
So, the closest answer to our calculated value is 10.4 seconds.
Therefore, the correct option is Option C: 10.4 sec
Here's the formula we'll use: T = 2π * √(k² / (g * GM))
Where:
T is the time of rolling (what we want to find).
k is the radius of gyration (given as 4 m). This tells us how the ship's mass is distributed around its center of rotation. A larger radius means more resistance to rolling.
g is the acceleration due to gravity (approximately 9.81 m/s²). This is a constant.
GM is the metacentric height (given as 0.6 m). This is a measure of the ship's initial stability. A larger GM means the ship is more stable (resists rolling more), but can also mean a quicker, more uncomfortable roll. A smaller GM means less initial stability, potentially leading to capsizing if too small.
Now, let's plug in the values:
T = 2 * π * √(4² / (9.81 * 0.6))
T = 2 * π * √(16 / 5.886)
T = 2 * π * √2.718
T = 2 * π * 1.649
T ≈ 10.36 seconds
So, the closest answer to our calculated value is 10.4 seconds.
Therefore, the correct option is Option C: 10.4 sec