$a=\frac{F+f}{m}$
for roational motional about $C . M$ of
$R(F-f)=I \alpha$
$\alpha=\frac{R}{I}(F-f)$
For pure rolling $a=R \alpha$
$\frac{F+f}{m}=\frac{R^{2}}{I}(F-f)$
$f\left(1+\frac{m R^{2}}{I}\right)=F\left(\frac{m R^{2}}{I}-1\right)$
$f=\frac{\left(m R^{2}-I\right)}{m R^{2}+I} F$
For ring//thin pipe $I=m R^{2},$ so $f=0$ therefore for rolling of ring//thin pipe does not need friction. 
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$(a)$ Maximum current $(I_m)$ increases
$(b)$ Sharpness of the graph increases
$(c)$ Quality factor increases
$(d)$ Band width increases
