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.

Options

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)`

Answer

A, B, D

Explanation

(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`