Two wires as shown in the figure below, made of steel and have breaking stress of $$12 \times 10^8$$ N/m$$^2$$. Area of cross-section of upper wire is 0.008 cm$$^2$$ and of lower wire is 0.004 cm$$^2$$. The maximum mass that can be added to pan without breaking any wire is _______ kg. (take $$g = 10$$ m/s$$^2$$)

Breaking stress = $$12\times10^8N/m^2$$

Areas:
$$upper=0.008cm^2=8\times10^{-7}m^2$$
$$lower=0.004cm^2=4\times10^{-7}m^2$$

step 1: max tension each wire can bear

upper wire:

$$T_u=σA=12\times10^8\times8\times10^{-7}=960N$$

lower wire:

$$T_l=12\times10^8\times4\times10^{-7}=480N$$

step 2: tensions in wires

let mass added = mmm

lower wire carries:

$$T_l=(10+m)g=(10+m)\times10$$

=100+10m

limit:

$$100+10m\le480\Rightarrow m\le38$$

upper wire carries total mass:

$$30+10+m=40+m$$

$$T_u=(40+m)\times10=400+10m$$

limit:

$$400+10m\le960\Rightarrow m\le56$$

step 3: final

smaller limit governs → m=38