The maximum torque a bolt can withstand without breaking is 100 N m. A mechanic tightens the bolt with a spanner 0.25 m long. What is the ..maximum...

The force causes a translatory motion in a body and similarly torque causes the rotatory motion. In physics it is also called the moment of the force about a point or pivot. The magnitude of torque is the product of the force and the perpendicular distance of the pivot from the force. So , if F is the force applied at angle  x to the arm of length r of the spanner, about a pivot (here the bolt), then the torque T = r * Fsinx  and is expressed in units od Newton meter. So, the torque  the mechanic can exert  through the spanner arm length r=0.25 m, which the bolt could sustain is given by:

100Nm > 0.25 F sinx, or F < 100Nm/(0.25m sinx) = 400 N/sin x

So at 90 degree, sinx = 1.Threfore, F should be within 400 N.

If uses his force, at angle 70 degree to the spanner, he can use  a focce  still higher  but less than 400/sin70 = 425.67 N.

If he uses the spanner of lesser arm length say, 0.20m, then

it  requires higher force  to produce the required torque and the force is given by: F < 100Nm/(0.20m*sin x) = 500N/sinx. So it is less likely that he applies higher force which exhuasts him. Still a lower arm of  spanner ,say 0.10m , if he utilises, it requires, a force F < 100Nm/(0.10m*sinx) =1000N/sinx , which is still  more difficult and strenuous for the mechanic to exert and he is still less likely to break the bolt.