combined translatory and rotatory motion ,Pure rolling motion questions with solutions

Showing 1–10 of 91 questions

• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A sphere is placed rotating with its centre initially at rest in a corner as shown in figure (a) and (b). Coefficient of friction between all surfaces and the sphere is 1/3. Find the ratio of the frictional force fa fb by ground in situations (a) and (b).

  

  Options

  • Option A

    1

  • Option B

    9/10

  • Option C

    10/9

  • Option D

    none

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• ParagraphmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A ring of mass M and radius R slides with speed v₀ and suddenly enters a rough horizontal surface with coefficient of friction µ, as shown.

  

  Sub-question 1

  Choose the correct alternative(s):-

  Select all that apply

  • Option A

    The linear distance moved by the centre of mass before the ring starts rolling is 3v₀²/(8µg).

  • Option B

    The net work done by friction is -3mv₀²/8.

  • Option C

    The loss in kinetic energy of the ring is mv₀²/4.

  • Option D

    The gain in rotational kinetic energy is mv₀²/8.

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  Two particles of mass m move with equal speed v₀ in opposite directions and strike the ends of a rigid massless rod of length ℓ perpendicular to the rod. They stick to the rod. What is the tension in the rod during the subsequent rotation?

  

  Options

  • Option A

    2mv₀²/ℓ

  • Option B

    mv₀²/ℓ

  • Option C

    mv₀²/(2ℓ)

  • Option D

    4mv₀²/ℓ

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• ParagraphmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A simplified bicycle of mass M has wheelbase w. Its center of mass is midway between the tyre contact points at height h. Air resistance is ignored. Case 1: the bicycle accelerates rightward with acceleration a and both tyres roll purely. Case 2: it moves rightward but slows with acceleration magnitude a while both tyres skid; coefficient of sliding friction at each tyre is µ.

  

  Sub-question 1

  The direction of friction on the tyres is

  Options

  • Option A

    forward on both

  • Option B

    backward on both

  • Option C

    forward on front & backward on rear

  • Option D

    forward on rear & backward on front.

  Sub-question 2

  What is the maximum value of μ so that both tyres remain in contact with the ground?

  Options

  • Option A

    w/2h

  • Option B

    h/2w

  • Option C

    2h/w

  • Option D

    w/h

  Sub-question 3

  What is the maximum value of a so that both tyres remain in contact with the ground?

  Options

  • Option A

    wg/h

  • Option B

    wg/2h

  • Option C

    hg/2w

  • Option D

    2hg/w

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)-

  

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A vertical force P is applied tangentially to the uniform cylinder shown. The coefficient of static friction at both contacts is 0.500. If the cylinder weight is Fg, what is the maximum P for which the cylinder does not rotate?

  

  Options

  • Option A

    Fg/4

  • Option B

    3Fg/8

  • Option C

    Fg/2

  • Option D

    5Fg/8

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• ParagraphmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  For the following three situations, a cylinder is pulled on a rough horizontal surface by a constant force F. Determine the direction of friction.

  Sub-question 1

  A cylinder of mass M and radius R is pulled horizontally by a force F. The friction force can be given by which of the following diagrams:-

  

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    Cannot be interpreted

  Sub-question 2

  A cylinder is pulled horizontally by a force F acting at a point below the centre of mass of the cylinder, as shown in figure. The friction force can be given by which of the following diagrams:-

  

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    Cannot be interpreted

  Sub-question 3

  A cylinder is pulled horizontally by a force F acting at a point above the centre of mass of the cylinder, as shown in figure. The friction force can be given by which of the following diagrams

  

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    Cannot be interpreted

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A wheel rolls without slipping on a horizontal surface. The speed of the particle at the highest point of the rim is 8 m/s. The speed of a particle on the rim that is at the same level as the centre of the wheel is:

  Options

  • Option A

    8√2 m/s

  • Option B

    8 m/s

  • Option C

    4√2 m/s

  • Option D

    4 m/s

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• MCQmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A solid spherical ball rolls without slipping on a table. Find the ratio of its rotational kinetic energy to its total kinetic energy.

  Options

  • Option A

    1/2

  • Option B

    1/6

  • Option C

    7/10

  • Option D

    2/7

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• NumericmediumRotational Motioncombined translatory and rotatory motion ,Pure rolling motion

  A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m s⁻¹ at t = 0 on a rough horizontal surface. It starts with purely sliding motion. After 2 s it acquires pure rolling. The total kinetic energy of the disc after 2 s will be ______ J. [Coefficient of friction = 0.3, g = 10 m s⁻²]

  

  Your answer

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