torque and rotational equilibrium questions with solutions

Showing 1–10 of 40 questions

• NumericmediumRotational Motiontorque and rotational equilibrium

  A particle of mass 1 kg is acted on by $\vec{F}$ = -k(x î + y ĵ), where k = 1 kg s⁻². At t = 0, $\vec{r}$ = (î/√2 + √2 ĵ) m and $\vec{v}$ = (-√2 î + √2 ĵ + (2/π)k̂) m s⁻¹. Ignore gravity. When z = 0.5 m, find x vᵧ - y vₓ in m² s⁻¹.

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  JEE Advanced 2022

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• MCQmediumRotational Motiontorque and rotational equilibrium

  In the given figure a uniform wheel of radius 30cm rests against a rigid rectangular block 15cm high. All the surfaces are smooth. The wheel weighs 1000 N. The minimum pull P through the center which will turn the wheel over the block is:-

  

  Options

  • Option A

    500√3 N

  • Option B

    1000√3 N

  • Option C

    1000 N

  • Option D

    400√3 N

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• MCQmediumRotational Motiontorque and rotational equilibrium

  A weightless rod is acted on by upward parallel forces of 2N and 4N at ends A and B respectively. The total length of the rod is AB = 3m. To keep the rod in equilibrium a force of 6N should act in the following manner:

  Options

  • Option A

    Downwards at any point between A and B.

  • Option B

    Downwards at mid point of AB.

  • Option C

    Downwards at a point C such that AC = 1m.

  • Option D

    Downwards at a point D such that BD = 1m.

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• MCQeasyRotational Motiontorque and rotational equilibrium

  If $\vec{F}$ acts at position vector $\vec{r}$ , with torque $\vec{\tau}$ about the origin, which relations are always correct?

  Options

  • Option A

    $\vec{r}.\vec{\tau}$≠0 and $\vec{F}.\vec{\tau}$=0

  • Option B

    $\vec{r}.\vec{\tau}$>0 and $\vec{F}.\vec{\tau}$<0

  • Option C

    $\vec{r}.\vec{\tau}$=0 and $\vec{F}.\vec{\tau}$=0

  • Option D

    $\vec{r}.\vec{\tau}$=0 and $\vec{F}.\vec{\tau}$≠0

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• Multi-correctmediumRotational Motiontorque and rotational equilibrium

  One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight αW is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of 2√2 W. Which of the following statement(s) is(are) correct ?

  

  Select all that apply

  • Option A

    The vertical component of reaction force at O does not depend on α.

  • Option B

    The horizontal component of reaction force at O is equal to W for α = 0.5.

  • Option C

    The tension in the rope is 2W for α = 0.5.

  • Option D

    The rope breaks if α > 1.5.

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• MCQmediumRotational Motiontorque and rotational equilibrium

  A uniform rod of length l is placed symmetrically on two walls as shown in figure. The rod is in equilibrium. If N₁ and N₂ are the normal forces exerted by the walls on the rod then:-

  

  Options

  • Option A

    N₁ > N₂

  • Option B

    N₁ < N₂

  • Option C

    N₁ = N₂

  • Option D

    N₁ and N₂ are vertical

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• MCQmediumRotational Motiontorque and rotational equilibrium

  A rod of weight w is supported by two parallel knives at end points A and B and is in equilibrium in a horizontal position. The knives are at a distance 'd' from each other. The centre of mass of the rod is at a distance 'x' from A.

  Options

  • Option A

    Normal reaction at A = wx/d

  • Option B

    Normal reaction at A = w(d-x)/d

  • Option C

    Normal reaction at B = wx/d

  • Option D

    Normal reaction at B = w(d-x)/d

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• MCQmediumRotational Motiontorque and rotational equilibrium

  A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle θ from the horizontal as shown in the figure below. The maximum value of θ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) -

  

  Options

  • Option A

    sinθ=r/R

  • Option B

    tanθ=r/R

  • Option C

    sinθ=r/2R

  • Option D

    cosθ=r/2R

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• MCQmediumRotational Motiontorque and rotational equilibrium

  In the shown equilateral triangle ABC with centre O, forces F₁, F₂ and F₃ act along the directed sides AB, BC and AC. If net torque about O vanishes, find F₃.

  

  Options

  • Option A

    F₁+F₂

  • Option B

    F₁-F₂

  • Option C

    (F₁+F₂)/2

  • Option D

    2(F₁+F₂)

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• NumericmediumRotational Motiontorque and rotational equilibrium

  A uniform metre scale is supported on two index fingers initially at 0.00 cm and 90.00 cm. As the fingers are slowly moved toward the centre, they alternately stick and slip. The right finger eventually stops at a distance denoted xR from the 50.00 cm mark. Given µₛ = 0.40 and µₖ = 0.32, find xR in cm.

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