A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc,

Options

A. velocity is `v`, acceleration is zero
B. velocity is zero, acceleration is zero
C. velocity is `v`, acceleration is `v^(2)//R`
D. velocity is `0`, acceleration is `v^(2)//R`

Answer

D

Explanation

As the disc is in combined rotation and translation each point has a tangential velocity and a linear velocity in the forward direction. From the figure.
`V_("net")` (for the lowest point) ` =v`
`Romega=v-v_(0)` and acceleration `(v^(2))/R+0=(v^(2))/R`
(since the linear speed is constant)