friction and circular motion questions with solutions

Showing 1–10 of 67 questions

• MCQmediumCircular Motionfriction and circular motion

  An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop (in Km)?

  Options

  • Option A

    12 Km

  • Option B

    15 Km

  • Option C

    20 Km

  • Option D

    21 Km

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• MCQeasyCircular Motionfriction and circular motion

  A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [Take g = 10 m s⁻²]

  Options

  • Option A

    3.4 m s⁻¹

  • Option B

    22.4 m s⁻¹

  • Option C

    13 m s⁻¹

  • Option D

    17 m s⁻¹

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• NumericmediumCircular Motionfriction and circular motion

  A cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then find the minimum value of coefficient of friction between the cycle tyres and road. (g = 9.8 m/s²)

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• NumericeasyCircular Motionfriction and circular motion

  A circular road of radius 40 m is banked for a frictionless design speed of 20 m/s. Take g = 10 m/s². If tanθ = N/10, find N.

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• MCQmediumCircular Motionfriction and circular motion

  A cyclist travels at 18 km/h on a level road and takes a circular turn of radius 3 m without reducing speed. If µₛ=0.1 and g=10 m/s², will the cyclist slip?

  Options

  • Option A

    Yes, because v²/R≈8.33 m/s²>µg=1 m/s²

  • Option B

    No, because v²/R<µg

  • Option C

    No, because centripetal force is supplied by weight

  • Option D

    Yes, only if µ>1

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• MCQmediumCircular Motionfriction and circular motion

  A motorcycle crosses a convex circular overbridge of radius R and total arc length L at constant speed. Find: (a) the maximum speed for contact at the highest point; (b) if speed is 1/√2 times that value, the distance from the top where contact is lost; (c) the maximum uniform speed that maintains contact over the entire bridge.

  Options

  • Option A

    (a) √(Rg); (b) πR/3 from the top; (c) √[gR cos(L/2R)]

  • Option B

    (a) √(2Rg); (b) πR/2; (c) √(gR)

  • Option C

    (a) √(Rg/2); (b) πR/6; (c) √[2gR cos(L/R)]

  • Option D

    (a) √(Rg); (b) πR/6; (c) √[gR sin(L/2R)]

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• MCQmediumCircular Motionfriction and circular motion

  For a banked road of radius r and banking angle θ with coefficient of friction μ, the maximum possible speed is:

  Options

  • Option A

    √{gr(μ+tanθ)/(1-μtanθ)}

  • Option B

    √{gr(μ-tanθ)/(1-μtanθ)}

  • Option C

    √{gr(1+μtanθ)/(1-μtanθ)}

  • Option D

    √{gr(μ-tanθ)/(1+μtanθ)}

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• MCQmediumCircular Motionfriction and circular motion

  A car moves on a horizontal circular road of radius R while its speed increases at constant tangential acceleration a=dv/dt. If the tyre-road friction coefficient is µ, find the speed at which it skids.

  Options

  • Option A

    v=[(µ²g²-a²)R²]^(1/4)

  • Option B

    v=[(µ²g²+a²)R²]^(1/4)

  • Option C

    v=√(µgR)

  • Option D

    v=µgR/a

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• MCQmediumCircular Motionfriction and circular motion

  For a banked circular road of radius r, banking angle θ and coefficient of friction μ, the maximum safe speed is given by:

  Options

  • Option A

    $v_max²$ = rg(sinθ + μcosθ)/(cosθ - μsinθ)

  • Option B

    $v_max²$ = rg(sinθ - μcosθ)/(cosθ + μsinθ)

  • Option C

    $v_max²$ = rg tanθ

  • Option D

    $v_max²$ = μrg

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• Multi-correctmediumCircular Motionfriction and circular motion

  Which statements about a banked circular road are correct?

  Select all that apply

  • Option A

    At the design speed, friction can be zero

  • Option B

    The frictionless design speed is v₀ = √(rg tanθ)

  • Option C

    For speed lower than the design speed, friction can act up the slope

  • Option D

    For speed higher than the design speed, friction can act down the slope

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