Torque and Statics Balance Problem

[lemonlimesoap]

Homework Statement

Two pans of a balance are 50cm apart. If the fulcrum is displaced by 1cm what percentage is the true weight marked up?

Homework Equations

T=rFsinθ
F=mg

The Attempt at a Solution

I solved for torque of the fulcrum in a hypothetical situation where a mass of 1g is on one end and a mass of 2g on the other

First with the fulcrum in the center making the lever arms 25cm
T=T1+T2

T=7.3575Nm

then with the displaced fulcrum by 1cm. Making the lever arms 24cm and 26cm

T=7.4556Nm

finally i just did percent error

(7.4556Nm-7.3575Nm)/7.3575Nm *100= 1.3%

I'm pretty sure this is wrong since I was just winging it.

 

[tiny-tim]

hi lemonlimesoap!

Two pans of a balance are 50cm apart. If the fulcrum is displaced by 1cm what percentage is the true weight marked up?
…
I solved for torque of the fulcrum in a hypothetical situation where a mass of 1g is on one end and a mass of 2g on the other

nooo …

you're not being realistic about the way a balance works …

a balance works by being balanced …

you put an unknown mass in one pan, and known masses in the other pan until the torques are equal …

so start again, with 1g in one pan, and m in the other pan …

what is m ? ​