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Vimala Nazir Kale
Asked: 2022-10-29T03:45:52+05:30 In:

A sphere of mass `M` and radius r shown in the figure on a rough horizontal plane. At some instant it has translational velocity `v_(0)`, and rotational velocity about centre `v_(0)//2r`. The percentage change of translational velocity after the sphere start pure rolling:
image
A. `14.28%`
B. `7.14%`
C. `21.42%`
D. none

A sphere of mass `M` and radius r shown in the figure on a rough horizontal plane. At some instant it has translational velocity `v_(0)`, and rotational velocity about centre `v_(0)//2r`. The percentage change of translational velocity after the sphere start pure rolling:
image
A. `14.28%`
B. `7.14%`
C. `21.42%`
D. none
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  1. Correct Answer – A
    Initial angular momentum
    `L=2/5Mr^(2)((v_(0))/(2r))+Mrv_(0)=6/5Mrv_(0)` …………i
    The angular mometum about `A` is
    `=2/5Mr^(v/r)+Mrv=2/5Mr^(2)(v/r)+Mrv`……ii
    `v=6/7v_(0)`.
    `:. %` change of translation velocity
    `=[(v_(0)-6/7v_(0))/(v_(0))]xx100=1/7xx100=14.28%`

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