`Delta` some in tan , a disk of radius 1.0 m is performing rolling on a rough horizontal surface. The velocity of point C in this shown direction is `5 m//sec` :

Options

A. Instantaneous centre is at a distance 1.0 m below centre O
B. Instantaneous centre is at a distance `0.05 m` below centre O
C. Angular velocity of disc is `(5//sqrt2)` rad/sec
D. Velocity of centre of mass is `(5//sqrt2)` m/s

Answer

A, C, D

Explanation

`R = 1.0 m, " " M = 1.0 kg`
Velocity of COM = V
Angular velocity of disc `= omega`
1 is the instantaneous centre.
`tan 45^(@) = (O1)/(R)`
`OI = R tan 45^(@)`

` = R = 1.0`
`IC = R sqrt2 = sqrt2`
`omega = (V_(C))/(IC) = (5)/(sqrt2)` rad/sec
`V = (OI) omega = (1.0) ((5)/(sqrt2)) = (5)/(sqrt2) (m//sec)`