question based on pure rotation about fixed axis questions with solutions

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  A right triangular plate ABC of mass m is free to rotate in the vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A in equilibrium is:

  

  Options

  • Option A

    mg/3

  • Option B

    2mg/3

  • Option C

    mg/2

  • Option D

    mg

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• MCQeasyRotational Motionquestion based on pure rotation about fixed axis

  Angular displacement of a wheel is θ(t)=2t³-6t². At what time is net torque on it zero (constant I)?

  Options

  • Option A

    t=0.5 s

  • Option B

    t=0.25 s

  • Option C

    t=2 s

  • Option D

    t=1 s

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  A thin uniform hemispherical bowl of mass m and radius R is lying on a smooth horizontal surface. A horizontal force F is now applied perpendicular to the rim of the bowl (see figure). The instantaneous angular acceleration of the bowl will be:-

  

  Options

  • Option A

    20F/(3MR)

  • Option B

    10F/(3MR)

  • Option C

    40F/(3MR)

  • Option D

    6F/(5MR)

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• Multi-correctmediumRotational Motionquestion based on pure rotation about fixed axis

  Two particles each of mass m are attached at end points of a massless rod AB of length l. Rod is hinged at point C as shown. Rod is released from rest from horizontal position. At the instant when rod reaches its vertical position as shown, which of the following is/are CORRECT:-

  

  Select all that apply

  • Option A

    Speed at B = 3 × speed at A

  • Option B

    Net force on B = 6mg/5

  • Option C

    Angular acceleration = 0

  • Option D

    Both x and y components of hinge force are non-zero

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  Three particles A, B and C, each of mass m, form a rigid equilateral triangle of side ℓ hinged at A on a smooth horizontal table. The body rotates about A with angular speed ω. When BC is parallel to the x-axis, a force F is applied at B along BC. Which option gives the correct complete set: (i) hinge-force magnitude before F is applied, and immediately after applying F (ii) x-component and (iii) y-component of the hinge force?

  

  Options

  • Option A

    (i) mℓω²; (ii) -F/4; (iii) √3mℓω²

  • Option B

    (i) √3mℓω²; (ii) +F/4; (iii) √3mℓω²

  • Option C

    (i) √3mℓω²; (ii) -F/4; (iii) √3mℓω²

  • Option D

    (i) √3mℓω²; (ii) -F/2; (iii) √3mℓω²

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  A uniform rod of length ℓ and mass m pivots freely at one end A. It is released from rest from a horizontal position. Given I(A)=mℓ²/3, its initial angular acceleration is:

  

  Options

  • Option A

    gℓ/2

  • Option B

    (3/2)gℓ

  • Option C

    3g/(2ℓ)

  • Option D

    2g/(3ℓ)

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  An automobile moves at 54 km/h. A wheel has radius 0.45 m and moment of inertia 3 kg·m². If the vehicle stops uniformly in 15 s, find average braking torque on the wheel.

  Options

  • Option A

    6.66 N·m

  • Option B

    8.58 N·m

  • Option C

    10.86 N·m

  • Option D

    2.86 N·m

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• NumericmediumRotational Motionquestion based on pure rotation about fixed axis

  The door of an automobile is initially open and perpendicular to the body. The automobile accelerates at 2 ft/s² and the door width is 30 inches. Treat the door as a uniform rectangle and neglect friction. The speed of its outer edge, as seen by the driver when the door closes, is √n ft/s. Find n.

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• MCQmediumRotational Motionquestion based on pure rotation about fixed axis

  For the wheel shown, r₁=5 cm, r₂=30 cm and I=5100 kg·m² about the central axis. What is the angular acceleration?

  

  Options

  • Option A

    10⁻² rad/s² clockwise

  • Option B

    10⁻³ rad/s² anticlockwise

  • Option C

    10⁻² rad/s² anticlockwise

  • Option D

    10⁻³ rad/s² clockwise

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• Multi-correctmediumRotational Motionquestion based on pure rotation about fixed axis

  A rod is connected with the (rigid body) disc at centre of disc point 'P'. The disc can freely rotate about point P where it is hinged with rod and rod can rotate freely about fixed hinge Q. Now whole arrangement is released from horizontal position as shown in the diagram.

  

  Select all that apply

  • Option A

    Initial angular acceleration of disc = 0

  • Option B

    Initial angular acceleration of disc = 9g/(8ℓ)

  • Option C

    Angular speed of disc when rod becomes vertical = 0

  • Option D

    Angular speed = (3/2)√(g/ℓ) rad/s

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