Two wires shown in figure are made of the same material which has a breaking stress of `8xx10^(8) N/m^(2)`. The area of cross- section of the upper wire is `0.006 cm^(2)` and that of the lower wire is `0.003 cm^(2)`. The mass `m_(1) = 10 kg, m_(2) = 20 kg ` and the hanger is light . Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the load is increased ? ( Take `g = 10 m//s^(2))`

Explanation

Maximum tension that the upper wire tolerate =Breaking stress `xx` area
`T_(2)=8xx10^(8)xx0.006xx10^(-4)=482N`

Maximum tension on that the lower wire has
`T_(1)=8xx10^(8)xx0.003xx10^(-4)=240N`
we have, `T_(2)=T_(1)+200` and `T_(1)=100+mg`
`therefore T_(2)=300+mg`
`because T_(2) le 480`
`therefore 300+mg le 480` or `mg le 180` or `m le 18 kg`
Again `T_(1) le240` or `100+mg le 240`
or `m le 14 kg`
Maximum mass `m_("max")=14 kg` , when load is increased, `T_(1)` increase hence, lower wire will break.