centripital force and centrifugal force questions with solutions

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• NumericeasyCircular Motioncentripital force and centrifugal force

  A conical pendulum has a bob of mass 2 kg and its string makes 60° with the vertical. Take g=10 m/s². If the string tension is N newton, find N.

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• NumericmediumCircular Motioncentripital force and centrifugal force

  A particle of mass 2 kg moves on a smooth horizontal table in a circle of radius 0.5 m with angular speed 4 rad/s. It is attached to a string passing through a smooth hole at the centre of the table, and the other end supports a hanging mass M which remains stationary. Take g=10 m/s². If 10M=N, find N.

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• NumericmediumCircular Motioncentripital force and centrifugal force

  Two equal masses of 1 kg each are connected by a spring of force constant 10 N/m and natural length 1 m. They rotate about their common centre of mass with angular speed 2 rad/s. If the spring extension is x and 100x=N, find N.

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• A/RmediumCircular Motioncentripital force and centrifugal force

  Evaluate the following statements.

  Assertion

  Assertion (A): In a frame rotating with the radial groove, the outward radial acceleration of the bead can be described using centrifugal force.

  Reason

  Reason (R): In that rotating frame, the centrifugal pseudo force mω²r acts radially outward and gives the radial equation m(d²r/dt²)=mω²r.

  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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• NumericeasyCircular Motioncentripital force and centrifugal force

  A conical pendulum has string length 1.25 m and cosθ=0.8. Take g=π² m/s². If the square of its time period is N s², find N.

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• NumericeasyCircular Motioncentripital force and centrifugal force

  A bead is in a smooth radial groove of a disc rotating with constant angular speed 3 rad/s. At an instant its distance from the centre is 2 m. If its radial acceleration d²r/dt²=N m/s², find N.

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• MCQmediumCircular Motioncentripital force and centrifugal force

  A bead is initially at distance r₀ from the centre of a smooth radial groove on a disc rotating with constant angular speed ω. Its initial radial speed is zero. Its radial position after time t is:

  Options

  • Option A

    r = r₀ cosh(ωt)

  • Option B

    r = r₀ cos(ωt)

  • Option C

    r = r₀ sinh(ωt)

  • Option D

    r = r₀$e^(-ωt)$

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• MCQmediumCircular Motioncentripital force and centrifugal force

  A small bead can slide without friction in a radial groove of a horizontal disc rotating with constant angular speed ω. If r is the bead's distance from the centre, its radial equation of motion in an inertial frame is:

  Options

  • Option A

    d²r/dt² = ω²r

  • Option B

    d²r/dt² = -ω²r

  • Option C

    d²r/dt² = 2ω(dr/dt)

  • Option D

    d²r/dt² = 0

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• NumericmediumCircular Motioncentripital force and centrifugal force

  A conical pendulum has string length 5 m and its bob moves in a horizontal circle of radius 3 m. Take g=10 m/s². If ω²=N/2, find N.

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• MCQmediumCircular Motioncentripital force and centrifugal force

  A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be: (Take g = 10 m/s²)

  Options

  • Option A

    π/6

  • Option B

    π/2

  • Option C

    π/4

  • Option D

    π/3

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