PhysicsThe ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle ’θ’ without slipping and slipping down the incline without rolling is

The ratio of the accelerations for a solid sphere (mass ‘m’ and radius ‘R’) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

  1. A

    2:3

  2. B

    2:5

  3. C

    7:5

  4. D

    5:7

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    Solution:

    The solid sphere's roll down on an incline without slipping will have an acceleration of,

    aroll=gsinθ1+K2r2

    For solid sphere,

    K2=25R2K2r2=25

    aroll=gsinθ1+25=57gsinθ______(1)

    When a solid sphere slides down an incline without rolling, it accelerates due to,

    aslip=gsinθ_____(2)

    from equation 1 and 2 

    arollaslip=57aroll:aslip=5:7.

    Hence the correct answer is 5:7.

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