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The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually is
- a)same
- b)four times
- c)twice times
- d)one times
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The strain energy stored in a body due to suddenly applied load compar...
σ gradual = σ, σsudden = 2σ. The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually is four times.
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The strain energy stored in a body due to suddenly applied load compar...
Explanation:
When a load is applied to a body suddenly, the body undergoes deformation and the energy is stored in the form of strain energy. The strain energy is directly proportional to the square of the deformation.
When the same load is applied gradually, the deformation takes place gradually, and the strain energy stored in the body is less as compared to the sudden application of the load.
Let us consider a simple example to understand this concept.
Suppose a spring with a stiffness of k is compressed by a distance x. The strain energy stored in the spring can be calculated using the formula
U = 1/2 kx^2
Now, let us apply the load suddenly and compress the spring by the same distance x.
The deformation of the spring in this case will be sudden and the strain energy stored in the spring can be calculated using the same formula
U = 1/2 kx^2
But since the deformation is sudden, the value of x will be higher as compared to when the load is applied gradually. Let us assume that the value of x is y times higher when the load is applied suddenly.
So, the strain energy stored in the spring when the load is applied suddenly can be calculated as
U' = 1/2 ky^2(x^2)
= y^2 (1/2 kx^2)
= y^2 U
Therefore, the strain energy stored in the body due to suddenly applied load is twice the strain energy stored when the same load is applied gradually.
Hence, the correct answer is option B, twice.
When a load is applied to a body suddenly, the body undergoes deformation and the energy is stored in the form of strain energy. The strain energy is directly proportional to the square of the deformation.
When the same load is applied gradually, the deformation takes place gradually, and the strain energy stored in the body is less as compared to the sudden application of the load.
Let us consider a simple example to understand this concept.
Suppose a spring with a stiffness of k is compressed by a distance x. The strain energy stored in the spring can be calculated using the formula
U = 1/2 kx^2
Now, let us apply the load suddenly and compress the spring by the same distance x.
The deformation of the spring in this case will be sudden and the strain energy stored in the spring can be calculated using the same formula
U = 1/2 kx^2
But since the deformation is sudden, the value of x will be higher as compared to when the load is applied gradually. Let us assume that the value of x is y times higher when the load is applied suddenly.
So, the strain energy stored in the spring when the load is applied suddenly can be calculated as
U' = 1/2 ky^2(x^2)
= y^2 (1/2 kx^2)
= y^2 U
Therefore, the strain energy stored in the body due to suddenly applied load is twice the strain energy stored when the same load is applied gradually.
Hence, the correct answer is option B, twice.
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The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer?.
The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The strain energy stored in a body due to suddenly applied load compared to when it is applied gradually isa)sameb)four timesc)twice timesd)one timesCorrect answer is option 'B'. Can you explain this answer?.
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