A spring of spring constant k is suspended from the roof and a block of mass m is suspended at the other end of the spring. The block is suddenly released. Find the maximum elongation produced in the spring.
- A.2mg divided by k
- B.mg divided by 2k
- C.mg divided by k
- D.mg divided by 4k
Correct answer
Explanation
The correct answer is A, 2mg divided by k. When the block is released suddenly it falls freely at first, so at the lowest point its speed is zero and all the gravitational potential energy it has lost has gone into the spring. Equating mg multiplied by the extension with half of k multiplied by the square of the extension gives an extension of twice mg divided by k. Option C is wrong because mg divided by k is the static extension, the stretch obtained when the block is lowered gently so that it never acquires any speed; a suddenly applied load always gives twice the static value. Option B is wrong because half the static extension would require the block to be held part of the way down, which the question does not allow. Option D is wrong because a quarter of the static extension has no physical basis here. Remember the rule: sudden loading doubles the deflection.
Read the full article: Elasticity, Stress, Strain and Hooke's Law: Exam Notes
Practice Questions
View allHooke's law states that within the elastic limit
- A.Stress is directly proportional to strain
- B.Stress is inversely proportional to strain
- C.Strain is independent of stress
- D.Stress is proportional to the square of the strain
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Hooke found that so long as a body is not strained beyond its elastic limit, the restoring force per unit area rises in step with the fractional deformation, and the constant ratio of the two is called the modulus of elasticity.
Read the full explanation →The SI unit of stress is the
- A.Newton
- B.Joule
- C.Pascal
- D.Watt
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Stress is the restoring force divided by the area over which it acts, so its unit is the newton per square metre, and that combination is given the special name pascal, the same unit used for pressure.
Read the full explanation →Strain is a quantity that has
- A.The unit newton per square metre
- B.No unit and no dimensions
- C.The unit metre
- D.The same unit as energy
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Strain is defined as the change in a dimension divided by the original value of the same dimension, a length divided by a length or a volume divided by a volume, so the units cancel and only a pure number survives.
Read the full explanation →The ratio of longitudinal stress to longitudinal strain within the elastic limit is called
- A.Bulk modulus
- B.Modulus of rigidity
- C.Young's modulus
- D.Poisson's ratio
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It governs the stretching or compression of a wire or rod along its length and is obtained by dividing the force per unit area of cross section by the fractional change in length.
Read the full explanation →The reciprocal of the bulk modulus of a material is known as its
- A.Compressibility
- B.Rigidity
- C.Ductility
- D.Tenacity
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The bulk modulus measures how strongly a substance resists a change in volume under uniform pressure, so its reciprocal measures how readily the volume yields, and that quantity is called compressibility.
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