angular shm and its time period questions with solutions

Showing 1–10 of 11 questions

• NumericmediumSimple Harmonic Motionangular shm and its time period

  A simple pendulum of length 1 m is inside a vehicle accelerating horizontally at 7.5 m/s². Take g = 10 m/s². If the square of the angular frequency about the new equilibrium is N/4 s⁻², find N.

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• MCQmediumSimple Harmonic Motionangular shm and its time period

  Statement I: A pendulum is taken from Earth to a planet having four times Earth's mass and twice Earth's radius; its time period remains the same. Statement II: The time period of a simple pendulum depends only on the gravity of the planet.

  Options

  • Option A

    Statement I is true but Statement II is false

  • Option B

    Statement II is true but Statement I is false

  • Option C

    Both statements are false

  • Option D

    Both statements are true

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• MCQeasySimple Harmonic Motionangular shm and its time period

  Using a simple pendulum experiment g is determined by measuring its time period T. Which of the following plots represent the correct relation between the pendulum length L and time period T ?

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    

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• MCQeasySimple Harmonic Motionangular shm and its time period

  A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is _____cm. [Assume that the mass of the pendulum remains same.]

  Options

  • Option A

    120

  • Option B

    0.75

  • Option C

    7.5

  • Option D

    15

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• MCQeasySimple Harmonic Motionangular shm and its time period

  A body performs angular simple harmonic motion about a fixed axis with angular amplitude θ₀ and time period T. At an instant its angular displacement is +θ₀/2 and it is moving towards the positive angular extreme +θ₀. How much additional time is required to reach the extreme?

  Options

  • Option A

    T/12

  • Option B

    T/8

  • Option C

    T/6

  • Option D

    T/4

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• NumericmediumSimple Harmonic Motionangular shm and its time period

  A uniform rod of length 1.5 m is suspended from one end and performs small angular oscillations in a vertical plane. Take g = 10 m/s². If the square of its angular frequency is N s⁻², find N.

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• A/RmediumSimple Harmonic Motionangular shm and its time period

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  A simple pendulum inside a uniformly accelerating vehicle can still execute small SHM about a shifted equilibrium direction.

  Reason

  In the accelerating frame, gravity and the constant pseudo-acceleration combine to produce a constant effective gravity vector.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• Multi-correctmediumSimple Harmonic Motionangular shm and its time period

  Which statements are correct for angular SHM and physical pendulums under the small-angle approximation?

  Select all that apply

  • Option A

    A physical pendulum satisfies Iθ̈ = -Mgdθ.

  • Option B

    Its time period is 2π√[I/(Mgd)].

  • Option C

    A torsional oscillator satisfies Iθ̈ = -Cθ.

  • Option D

    A torsional oscillator has time period 2π√(I/C).

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• MCQeasySimple Harmonic Motionangular shm and its time period

  Assertion: At the peak of a mountain, the time period of a pendulum increases. Reason: The time period of a pendulum increases when g decreases.

  Options

  • Option A

    Assertion is correct, Reason is incorrect

  • Option B

    Assertion is incorrect, Reason is correct

  • Option C

    Assertion is incorrect, Reason is incorrect

  • Option D

    Assertion is correct, Reason is correct

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• MCQmediumSimple Harmonic Motionangular shm and its time period

  A simple pendulum of length l is suspended inside a vehicle accelerating horizontally with constant acceleration a. After the bob reaches its new equilibrium direction, it is displaced through a small angle about that direction and released. What is the time period of small oscillations?

  Options

  • Option A

    2π√(l/g)

  • Option B

    2π√[l/√(g²+a²)]

  • Option C

    2π√[l/(g+a)]

  • Option D

    2π√[l/(g-a)]

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