A wheel rolls purely between a rough horizontal surface below it and a horizontal plank above it under the action of a horizontal force `F` applied on the plank. If at any time `vec(v)_(p)` and `vec(v)_(c)` represent velocity of plank and velocity and `vec(a)_(p)` and `vec(a)_(c)` represent acceleration of plank and acceleration of centre of mass of wheel respectively then which of the following is `//` are correct.

Options

A. `|vec(v)_(p)|=2|vec(v)_(c)|`
B. `|vec(a)_(p)|=2|vec(a)_(c)|`
C. `|vec(v)_(p)|=|vec(v)_(b)|`
D. `|vec(a)_(p)|=|vec(a)_(b)|`

Answer

A, B

Explanation

For pure rolling of wheel wrt horizontal surface below it For pure rolling of wheel wrt plank

`V_(P)=V_(c)+Romega=2V_(e)`
`:. (dv_(p))/(dt)=(2dv_(c))/(dt), a_(p)=2a_(c)`