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Consider a sphere of mass 'm' radius 'R'...

Consider a sphere of mass 'm' radius 'R' doing pure rolling motion on a rough surface having velocity `vec(v)_(0)` as shown in the figure. It makes an elastic impact with the smooth wall and moves back and starts rolling after some time again.

A

change in angular momentum about `O` in the entire equals `2mv_(0)R` in magnitude.

B

momentum of impulse provided by the wall during impact about`O` equals `2mv_(0)R` in magnitude.

C

final velocity of ball will be `3/7 vec(v)_(0)`

D

final velocity of ball will be `-3/7 vec(v)_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
(at the point of pure rolling)
Taking angular momentum about the point `P`
`I omega_(0)-mV_(0)R=I omega+mVRrArr`
`2/5 mR^(2)xx(V_(0))/R-mV_(0)R=2/5 mR^(2)xxV/R+mVR`
`rArrV =-(3V_(0))/7`
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Knowledge Check

  • A solid cylinder of mass M and radius R pure rolls on a rough surface as shown in the figure. Choose the correct alternative (s).

    A
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    B
    The acceleration of the centre of mass is `(2)/(3)F/(M)`
    C
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    D
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    disk
    B
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    D
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    A
    `(mV_(0)^(2))/(2)-(mV_(0)^(2))/(pi)`
    B
    `(mv_(0)^(2))/(2)+(mv_(0)^(2))/(pi)`
    C
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    D
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