A system of two cylinders fixed to each other is free to rotate about a frictionless axis through the common center of the cylinders and perpendicular to the page. A rope wrapped around the cylinder of radius 2.50 m exerts a force of 4.49 N to the right on the cylinder. A rope wrapped around the cylinder of radius 1.14 m exerts a force of 9.13 N downward on the cylinder. What is the magnitude of the net torque acting on the cylinders about the rotation axis? Answer in three decimal places.

Explanation:

Because torque is a vector quantity , the direction of torque is considered along the axis of rotation .

In first case force is applied in the right direction , thus the torque will be in upwards direction .

The magnitude of torque is = force x perpendicular distance between point of application of force and axis of rotation .

Thus in this case τ₁ = 4.49 x 2.50 = 11.25 N-m

Similarly , torque on second cylinder τ₂ = 91.3 x 1.14 = 104.08 N-m

Here force is applied downwards direction , thus the direction of torque is in the plane of page .

The torque is a vector quantity . The net torque can be found

τ = =  331.402 N-m

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .