In the figure given below, a roller of diameter $ 0.4 \mathrm{~m} $ is raised on the pavement $ X \mathrm{Y} $ by forces $ F_{1} $ and $ F_{2} $ each of magnitude 10 $ N $. Compare the torques produced by the two forces."

${F}_{1}={F}_{2}=10N$

Perpendicular distance of the point of rotation X from the force ${F}_{1}$ is ${d}_{1}$ = 0.4 m (equal to the diameter of the circle) while that of force ${F}_{2}$ is ${d}_{2}=\frac{1}{2}\times 0.4m=0.2m$ (equal to the radius of the circle).

We know that the torque of the force is the product of force and the perpendicular distance between the force and the point about which the object is rotated.

$\frac{Torque\ produced\ by\ force\ {F}_{1}}{Torque\ produced\ by\ force\ {F}_{2}}=\frac{{F}_{1}\times {d}_{1}}{{F}_{2}\times {d}_{2}}$