JEE MainPhysicsProperties of MatterMCQ+4 / −1
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 103 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 1011 Pa, g = 9.8 m/s2]
- A3.60 10 8
- B2.60 10 7
- C1.87 10 3
- D7.07 10 4
View written solutionFree
Correct answer: B
- Given data
- Mass of structure:
- Number of identical columns:
- Inner radius of each hollow cylinder:
- Outer radius of each hollow cylinder:
- Young's modulus of steel:
- Acceleration due to gravity:
We need the compression strain in each column.
- Load supported by each column
Since the load is uniformly distributed among 4 identical columns,
First calculate total weight:
So force on each column:
- Cross-sectional area of each hollow column
For a hollow cylinder,
Substitute values:
- Stress in each column
- Compression strain
Using
So,
- Match with options
The calculated compression strain is
So the correct option is B.
- Comparison with stored correct answer
Stored correct answer: B
Our derived answer: B
They match.
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