relative angular velocity and radius of curvature questions with solutions

Showing 1–10 of 21 questions

• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  At an instant, a particle has speed 12 m/s and acceleration magnitude 6 m/s². The angle between velocity and acceleration is 60°. If the radius of curvature is 8√N m, find N.

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  Two particles start together and move in the same direction around a circle with periods 4 s and 6 s. During the first 24 s, excluding t = 0 but including t = 24 s, if they meet N times, find N.

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• NumericeasyCircular Motionrelative angular velocity and radius of curvature

  A projectile has horizontal velocity component 20 m/s. At a certain instant its vertical velocity component is zero. Take g = 10 m/s². If its radius of curvature at that instant is N m, find N.

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• Multi-correctmediumCircular Motionrelative angular velocity and radius of curvature

  For an ideal projectile moving under gravity only, which statements are correct?

  Select all that apply

  • Option A

    Radius of curvature at the highest point is finite

  • Option B

    Normal acceleration at the highest point equals g

  • Option C

    At the highest point R = vₓ²/g

  • Option D

    Radius of curvature must decrease throughout the upward journey

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• NumericeasyCircular Motionrelative angular velocity and radius of curvature

  Three particles A, B and C start simultaneously from the same point and move in the same direction with periods 2 s, 3 s and 4 s respectively. If all three first meet again at the starting point after N seconds, find N.

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• MCQmediumCircular Motionrelative angular velocity and radius of curvature

  A projectile is projected from the ground with speed 20 m/s at an angle 60° above the horizontal. Neglect air resistance and take g = 10 m/s². The radius of curvature of its trajectory at the highest point is:

  Options

  • Option A

    5 m

  • Option B

    10 m

  • Option C

    20 m

  • Option D

    40 m

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  A projectile is projected with speed 20 m/s at an angle 60° above the horizontal. Take g = 10 m/s². If the radius of curvature at the point of projection is N m, find N.

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• MCQmediumCircular Motionrelative angular velocity and radius of curvature

  At an instant, the velocity and acceleration of a particle make an angle θ. If its speed is v and acceleration magnitude is a, the radius of curvature is:

  Options

  • Option A

    v²/a

  • Option B

    v²/(a cosθ)

  • Option C

    v²/(a sinθ)

  • Option D

    va/sinθ

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  A particle moves along a curved path. At a certain point its speed is 6 m/s and total acceleration is 5 m/s². Its speed varies with arc length s according to v² = 16 + 6s. If the radius of curvature at that point is N m, find N.

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• NumericmediumCircular Motionrelative angular velocity and radius of curvature

  Particles A and B move in the same direction with angular speeds 7 rad/s and 3 rad/s. Initially B is 120° ahead of A. If A first catches B after π/N seconds, find N.

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