Question

why are spanners with long handles useful in opening nuts of a truck wheel as compared to spanner with small handles

Answer 1

While using spanners, we use torque (turning effect of force) which is termed as the product of perpendicular distance of the line of action of force from axis of rotation and magnitude of force.

In case of long spanners the length is more so the torque required is less but in case of small spanners length is small so large torque is required. Hence we use large spanners instead of small spanners.