Question:
A ship of 4000 m\(^3\) displacement has a block coefficient of 0.8.
If the beam is 0.1 times the length and twice the draught, then the length of the ship is ______ m (answer in integer).
A ship of 4000 m\(^3\) displacement has a block coefficient of 0.8.
If the beam is 0.1 times the length and twice the draught, then the length of the ship is ______ m (answer in integer).
If the beam is 0.1 times the length and twice the draught, then the length of the ship is ______ m (answer in integer).
Show Hint
Write beam and draught as fractions of length, then use the block coefficient volume formula.
Updated On: Jul 28, 2026
Show Solution
Verified By Collegedunia
Correct Answer: 100
Solution and Explanation
Step 1: Write the beam and draught in terms of length.
The beam is given as \(B = 0.1L\), and it is also twice the draught, so \(T = B/2 = 0.05L\).
Step 2: Use the displacement volume formula.
The displacement volume of a ship is \(\nabla = C_b \, L \, B \, T\), where \(C_b\) is the block coefficient. Substituting \(B\) and \(T\) in terms of \(L\): \(\nabla = C_b \, L \, (0.1L)(0.05L) = 0.005 \, C_b \, L^3\).
Step 3: Plug in the known values and solve for L.
\(4000 = 0.005 \times 0.8 \times L^3 = 0.004 \, L^3\), so \(L^3 = 4000/0.004 = 1{,}000{,}000\), giving \(L = 100\) m.
Final Answer:
The length of the ship is 100 m, matching the official key. \[ \boxed{L = 100 \text{ m}} \]
The beam is given as \(B = 0.1L\), and it is also twice the draught, so \(T = B/2 = 0.05L\).
Step 2: Use the displacement volume formula.
The displacement volume of a ship is \(\nabla = C_b \, L \, B \, T\), where \(C_b\) is the block coefficient. Substituting \(B\) and \(T\) in terms of \(L\): \(\nabla = C_b \, L \, (0.1L)(0.05L) = 0.005 \, C_b \, L^3\).
Step 3: Plug in the known values and solve for L.
\(4000 = 0.005 \times 0.8 \times L^3 = 0.004 \, L^3\), so \(L^3 = 4000/0.004 = 1{,}000{,}000\), giving \(L = 100\) m.
Final Answer:
The length of the ship is 100 m, matching the official key. \[ \boxed{L = 100 \text{ m}} \]
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