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Rotational Motion question

2002 · Shift 0 · Q181
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Rotational Motion question

2002 · Shift 0 · Q181

JEE MainPhysicsRotational MotionMCQ+4 / −1
A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)
  1. A
    solid sphere
  2. B
    hollow sphere
  3. C
    ring
  4. D
    all same
View written solutionFree

Correct answer: D

  1. Identify the physical situation

    The bodies are released on an inclined plane which is stated to be frictionless.

    Also, it is explicitly mentioned: no rolling.

    Therefore, the objects will simply slide down the incline.

  2. For motion on a frictionless incline

    The forces on any body are:

    • Weight: mgmgmg
    • Normal reaction: NNN

    Resolve weight along the incline: F∥=mgsin⁡θF_\parallel = mg\sin\thetaF∥​=mgsinθ

    Since there is no friction, this is the only force causing motion along the plane.

  3. Apply Newton's second law

    ma=mgsin⁡θma = mg\sin\thetama=mgsinθ

    So, a=gsin⁡θa = g\sin\thetaa=gsinθ

  4. Dependence on shape?

    The acceleration a=gsin⁡θa = g\sin\thetaa=gsinθ does not depend on:

    • mass
    • radius
    • moment of inertia
    • shape of the object

    Since there is no rolling, rotational inertia is irrelevant.

  5. Compare the given bodies

    • Solid sphere: a=gsin⁡θa = g\sin\thetaa=gsinθ
    • Hollow sphere: a=gsin⁡θa = g\sin\thetaa=gsinθ
    • Ring: a=gsin⁡θa = g\sin\thetaa=gsinθ

    Hence, all have the same acceleration.

  6. Evaluate options

    • A: solid sphere — incorrect
    • B: hollow sphere — incorrect
    • C: ring — incorrect
    • D: all same — correct

Final Answer

D: all same\boxed{\text{D: all same}}D: all same​

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