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NEET Physics: oscillations of a spring restoring force and force constant Practice Questions

14 free multiple-choice questions on oscillations of a spring restoring force and force constant (Oscillations and Waves) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.

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  1. Q1. A spring obeys Hooke's law. If the extension of the spring is doubled, what happens to the restoring force exerted by the spring?

    • AThe restoring force is doubled
    • BThe restoring force becomes four times
    • CThe restoring force is halved
    • DThe restoring force remains the same
    Show answer & explanation

    Correct answer: A — The restoring force is doubled

    According to Hooke's law, the restoring force (F) is directly proportional to the extension (x), i.e., F = kx. If the extension is doubled, the force exerted by the spring is also doubled.

  2. Q2. If the amplitude of oscillation of a mass attached to a spring is increased, how does the period of oscillation change?

    • AIt decreases
    • BIt depends on the spring constant only
    • CIt remains unchanged
    • DIt increases
    Show answer & explanation

    Correct answer: C — It remains unchanged

    The period of oscillation for a mass-spring system is given by T = 2π√(m/k). Since the period depends only on the mass (m) and the force constant (k), changing the amplitude does not affect the period.

  3. Q3. The constant 'k' in Hooke's Law (F = -kx) represents which physical property of the spring?

    • AElastic potential energy
    • BForce constant or spring constant
    • CAcceleration due to gravity
    • DMass of the spring
    Show answer & explanation

    Correct answer: B — Force constant or spring constant

    The constant 'k' is known as the force constant or spring constant, which measures the stiffness of the spring.

  4. Q4. What is the SI unit of the force constant (k)?

    • ANewton (N)
    • BJoule (J)
    • CNewton per meter (N/m)
    • DMeter (m)
    Show answer & explanation

    Correct answer: C — Newton per meter (N/m)

    Since Force (F) is in Newtons (N) and displacement (x) is in meters (m), the unit for the force constant k = F/x is N/m.

  5. Q5. If the force constant (k) of a spring is doubled while the displacement remains the same, what happens to the restoring force exerted by the spring?

    • AIt is doubled
    • BIt remains the same
    • CIt is quadrupled
    • DIt is halved
    Show answer & explanation

    Correct answer: A — It is doubled

    Since F = kx, if k is doubled and x is constant, the restoring force F will also be doubled.

  6. Q6. If the displacement of a spring is reduced to half its original value, how does the elastic potential energy stored in it change?

    • AIt becomes four times larger
    • BIt is reduced to one-fourth
    • CIt is halved
    • DIt is doubled
    Show answer & explanation

    Correct answer: B — It is reduced to one-fourth

    Since potential energy U ∝ x², if the displacement (x) is halved, the new energy will be proportional to (x/2)² = x²/4. Therefore, the potential energy is reduced to one-fourth of the original value.

  7. Q7. If a spring is stretched by a distance x, and a force F is applied, what is the relationship between the applied force and the spring constant k?

    • AF = x/k
    • BF = k/x
    • CF = x²/k
    • DF = kx
    Show answer & explanation

    Correct answer: D — F = kx

    According to Hooke's Law, the force F exerted by the spring is directly proportional to the extension x, meaning F = kx.

  8. Q8. Which physical quantity determines the stiffness of a spring?

    • AThe amplitude of oscillation
    • BThe coefficient of restitution
    • CThe total energy stored in the spring
    • DThe force constant
    Show answer & explanation

    Correct answer: D — The force constant

    The stiffness or elastic constant of a spring is defined by the force constant (k), which relates the restoring force to the displacement (F = kx).

  9. Q9. A spring obeys Hooke's law. If a force F is applied to stretch the spring by a distance x, the magnitude of the restoring force exerted by the spring is proportional to:

    • Ax
    • B1/x
    • Cx²
    • D1/x²
    Show answer & explanation

    Correct answer: A — x

    According to Hooke's law, the magnitude of the restoring force exerted by the spring is directly proportional to the extension x. Thus, F ∝ x (or F = kx).

  10. Q10. When a spring is displaced from its equilibrium position and allowed to oscillate, the potential energy stored in the spring is directly proportional to the square of the displacement. What is this relationship based on?

    • AKinetic energy of the oscillating body
    • BThe potential energy of the spring
    • CThe force exerted by the spring
    • DThe amplitude of oscillation
    Show answer & explanation

    Correct answer: B — The potential energy of the spring

    The elastic potential energy (U) stored in a spring is given by the formula U = 1/2 k x², where x is the displacement and k is the spring constant. Thus, the potential energy is proportional to the square of the displacement.

  11. Q11. The relationship between the time period of oscillation of a spring and its physical properties is governed by which constant?

    • AThe stiffness of the spring
    • BAmplitude of oscillation
    • CFrequency of the applied force
    • DMass of the oscillating body
    Show answer & explanation

    Correct answer: A — The stiffness of the spring

    The time period (T) of oscillation for a spring depends on the stiffness of the spring (which is related to the force constant, k) and the mass of the oscillating body. A stiffer spring (larger effective constant) results in a shorter time period for a given oscillation.

  12. Q12. Which quantity is directly proportional to the stiffness of a spring?

    • AForce constant (k)
    • BEnergy stored in the spring
    • CMass of the oscillating body
    • DAmplitude of oscillation
    Show answer & explanation

    Correct answer: A — Force constant (k)

    The force constant (k) is the measure of stiffness. A larger k means the spring exerts a larger restoring force for a given displacement.

  13. Q13. The restoring force exerted by a spring is always directed towards the equilibrium position. This implies that the force is:

    • AAlways negative
    • BVariable
    • CZero
    • DAlways positive
    Show answer & explanation

    Correct answer: A — Always negative

    The restoring force is proportional to the displacement (F ∝ -x). If the spring is stretched (positive x), the force is directed backward (negative direction), pulling it towards equilibrium.

  14. Q14. What is the restoring force exerted by a spring when it is displaced from its equilibrium position?

    • AProportional to the displacement
    • BZero
    • CInversely proportional to the displacement
    • DConstant
    Show answer & explanation

    Correct answer: A — Proportional to the displacement

    According to Hooke's Law, the restoring force (F) exerted by a spring is directly proportional to the displacement (x) from the equilibrium position (F = -kx).

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