A certain object is rolling without slipping on a horizontal surface. It was noted that its rotational kinetic energy equals its translational kinetic energy. Then the object is a-

  1. Ring
  2. Disc
  3. Solid sphere
  4. Cylinder

Answer (Detailed Solution Below)

Option 1 : Ring

Detailed Solution

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The correct answer is option 1) i.e. Ring

CONCEPT:

  • Rotational kinetic energy: Rotational kinetic energy is due to the motion of an object's rotation.

For a given fixed axis of rotation, the rotational kinetic energy is given by:

KE=12Iω2

Where I is the moment of inertia, ω is the angular velocity.

  • Let us consider that the mass of the objects are M and their radii is R. The moment of inertia about an axis passing through the centre of mass is as follows:

Solid sphere

F20 Jitendra K 3-6-2021 Swati D5

25MR2

Ring

F20 Jitendra K 3-6-2021 Swati D6

MR2

Disc

F20 Jitendra K 3-6-2021 Swati D7

12MR2

EXPLANATION:

  • The translational kinetic energy of an object of mass M and linear velocity v is given as KE=12Mv2

Rotational kinetic energyKE=12Iω2

  • Given that, rotational kinetic energy equals its translational kinetic energy.

12Mv2=12Iω2

M(rω)2=Iω2    (∵ linear velocity, v = rω)

Mr2=I

  • Therefore, the object is a ring.

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