The strain energy stored in a spring when it is subjected to maximum load without suffering permanent distortion is known as

Question

A rectangular section has width $b$ and depth $d$ and a symmetrical triangular section has base $b$ and depth $d$. The ratio of moment of inertia of rectangular section to that of triangular section with respect to their respective centroidal axis will be:

Answer 1

Strain energy stored elastically up to (but not beyond) the elastic limit is called proof resilience, this is the defining property being asked about.
Impact energy relates to sudden or shock loading conditions, not the amount of elastic energy a body can store.
Proof stress is a stress corresponding to a small permanent strain, not an energy term at all.
Modulus of resilience is proof resilience divided by the volume of the material, a related but different (per-unit-volume) quantity.
Since the question asks for the total strain energy stored up to the elastic limit, the matching term is proof resilience.

Answer 2

On a stress-strain diagram, elastic strain energy per unit volume equals the area under the straight-line (elastic) portion of the curve up to the elastic limit. Multiplying this area by the material's volume gives the total elastic energy the body can absorb before yielding. Checking each option against this diagram-based picture:

Impact energy: Corresponds to the kinetic energy transferred by a falling or moving mass at the instant of impact; it depends on the loading event, not on the area under the stress-strain curve, so it is not what is being described here.
Proof resilience: Is exactly the total area under the elastic (straight-line) part of the stress-strain diagram, up to the elastic limit, multiplied by the volume, giving the total energy stored just short of permanent set, which is precisely what the question describes.
Proof stress: Is a single point on the stress axis (the coordinate at a specified permanent strain), not an area under the curve, so it cannot represent stored energy.
Modulus of resilience: Is the area under the elastic portion of the curve alone, i.e. energy per unit volume, not multiplied out to the full volume of the body, so it describes a related but different (specific) quantity.

The area interpretation confirms the total elastic energy stored up to the point of permanent distortion is the proof resilience.

Therefore, the correct answer is proof resilience.

Answer 3

On a stress-strain diagram, elastic strain energy per unit volume equals the area under the straight-line (elastic) portion of the curve up to the elastic limit. Multiplying this area by the material's volume gives the total elastic energy the body can absorb before yielding. Checking each option against this diagram-based picture:

Impact energy: Corresponds to the kinetic energy transferred by a falling or moving mass at the instant of impact; it depends on the loading event, not on the area under the stress-strain curve, so it is not what is being described here.
Proof resilience: Is exactly the total area under the elastic (straight-line) part of the stress-strain diagram, up to the elastic limit, multiplied by the volume, giving the total energy stored just short of permanent set, which is precisely what the question describes.
Proof stress: Is a single point on the stress axis (the coordinate at a specified permanent strain), not an area under the curve, so it cannot represent stored energy.
Modulus of resilience: Is the area under the elastic portion of the curve alone, i.e. energy per unit volume, not multiplied out to the full volume of the body, so it describes a related but different (specific) quantity.

The area interpretation confirms the total elastic energy stored up to the point of permanent distortion is the proof resilience.

Therefore, the correct answer is proof resilience.

The strain energy stored in a spring when it is subjected to maximum load without suffering permanent distortion is known as

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The Correct Option is B

Approach Solution - 1

Approach Solution -2

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