angular impulse in pure rotation and rotational collision questions with solutions

Showing 1–10 of 20 questions

• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. If the rod has mass M = 2 kg, and length l = 1 m, the value of θ is approximately: (Take g = 10 m/s²)

  

  Options

  • Option A

    69°

  • Option B

    63°

  • Option C

    55°

  • Option D

    49°

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  JEE Mains 2020

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed ω about the vertical axis passing through the center of A. The angular momentum of B is nMωR² with respect to the center of A. Which of the following is the value of n?

  

  Options

  • Option A

    2

  • Option B

    5

  • Option C

    7/2

  • Option D

    9/2

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  JEE Advanced 2022

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• NumericmediumRotational Motionangular impulse in pure rotation and rotational collision

  A thin circular coin of mass 5 g and radius 4/3 cm lies initially in the horizontal xy-plane. It is tossed vertically upward by an impulse √(π/2)×10⁻² N·s applied 2/3 cm from its centre. The coin spins about a diameter and moves along +z. By the time it returns to its initial height, it completes n rotations. Find n. Take g = 10 m s⁻².

  

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  JEE Advanced 2023

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• NumericmediumRotational Motionangular impulse in pure rotation and rotational collision

  A thin uniform straight rod of mass 2 kg and length 1 m is free to rotate about its upper end when at rest. It receives an impulsive blow of 10 Ns at its lowest point, normal to its length as shown in figure. Find the kinetic energy of rod just after impact.

  

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  Two discs with the same moment of inertia I initially rotate at angular speeds ω₁ and ω₂ about their common axes. They are brought face-to-face and acquire the same final angular speed. Find rotational energy lost.

  Options

  • Option A

    ½I(ω₁+ω₂)²

  • Option B

    ¼I(ω₁-ω₂)²

  • Option C

    I(ω₁-ω₂)²

  • Option D

    (I/8)(ω₁-ω₂)²

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A thin circular ring of mass M and radius R rotates at angular speed ω. Two small particles each mass m are gently fixed at opposite ends of a diameter. Find final angular speed.

  Options

  • Option A

    ω(M-2m)/(M+2m)

  • Option B

    Mω/(M+2m)

  • Option C

    ω(M+2m)/M

  • Option D

    Mω/(M+m)

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is Md²/12. Then the angular speed of the system right after the collision is

  Options

  • Option A

    2v/d

  • Option B

    2v/(3d)

  • Option C

    v/d

  • Option D

    3v/(2d)

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A bar of mass M = 1.00 kg and length L = 0.20 m is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass m = 0.10 kg is moving on the same horizontal surface with 5.00 m·s⁻¹ speed on a path perpendicular to the bar. It hits the bar at a distance L/2 from the pivoted end and returns back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity ω. Which of the following statement is correct?

  Options

  • Option A

    ω = 6.98 rad·s⁻¹ and v = 4.30 m·s⁻¹

  • Option B

    ω = 3.75 rad·s⁻¹ and v = 4.30 m·s⁻¹

  • Option C

    ω = 3.75 rad·s⁻¹ and v = 10.0 m·s⁻¹

  • Option D

    ω = 6.80 rad·s⁻¹ and v = 4.10 m·s⁻¹

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• MCQmediumRotational Motionangular impulse in pure rotation and rotational collision

  A disc of inertia I₁ spins at ωᵢ. A second coaxial disc of inertia I₂ initially at rest is dropped onto it. Both eventually spin at the same speed. Find mechanical energy lost through friction.

  Options

  • Option A

    ½[I₂²/(I₁+I₂)]ωᵢ²

  • Option B

    ½[I₁²/(I₁+I₂)]ωᵢ²

  • Option C

    ½[(I₂-I₁)/(I₁+I₂)]ωᵢ²

  • Option D

    ½[I₁I₂/(I₁+I₂)]ωᵢ²

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• MCQeasyRotational Motionangular impulse in pure rotation and rotational collision

  A thin ring of mass M and radius r rotates at angular speed ω. Four particles each mass m are placed gently at the opposite ends of two perpendicular diameters. Find final angular speed.

  Options

  • Option A

    Mω/(4m)

  • Option B

    Mω/(M+4m)

  • Option C

    (M+4m)ω/M

  • Option D

    (M-4m)ω/(M+4m)

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  AIPMT 2003NEET

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