A uniform solid cylindrical roller of mass m is being pulled on...

By Newton's law of motion

$F - {f}_{s} = ma$ & & & & & & & & &...(i)

and torque, $τ = l\alpha$

where, $\alpha =$ tangential component of acceleration
$I = \text{moment of inertia}$

$⇒ fR = l\alpha$

fR = \dfrac{MR^{2}}{2} \cdot \dfrac{a}{R} \left[∴ I = \dfrac{MR^{2}}{2}\rightand \left, \alpha = \dfrac{a}{R}\right]</p><p>⇒ f = $\dfrac{ma}{2}</p><p>$∴ F = f + ma$</p><p>=\dfrac{ma}{2} +$ ma = $\dfrac{3ma}{2}$