Solution :

Considering the distance from centre to point A and B is $r_A$ and $r_B$ respectively.

Given :

$V_A=8 ~m/s$

$V_B=14 ~m/s$

$r_B-r_A=300 ~mm .....(i)$

We know that the relationship between angular velocity and linear velocity

At point A

$V_A=\omega × r_A=8 .....(ii)$

At point B

$V_B=\omega × r_B=14 .....(iii)$

Dividing equation (ii) and (iii), we get

$r_B=1.75 r_A$

Putting value of $r_B$ in equation (i), we get

$r_B=700 ~mm$

Thus, the radius is 700 mm.