The breaking force for a wire is F. For (i) two such wires put in parallel, and (ii) another wire ha

Question

The breaking force for a wire is F. For (i) two such wires put in parallel, and (ii) another wire having double the thickness, the breaking force\

Professor PC Thomas Classes · Answer

Breaking stress is a constant for a material. Breaking force depends on the diameter\ Original case:-\ Breaking force $=\mathrm{F}$\ Let area $=\mathrm{A}$\ Breaking stress $=\frac{\mathrm{F}}{\mathrm{A}}$\ Case I:- Two such wires\ Breaking force $=\mathrm{F}_{1}$\ Area $=2 \mathrm{~A}$\ Breaking stress $=\frac{\mathrm{F}_{1}}{2 \mathrm{~A}}$\ From (1) and (2) $\frac{\mathrm{F}_{1}}{2 \mathrm{~A}}=\frac{\mathrm{F}}{\mathrm{A}} \quad \mathrm{F}_{1}=2 \mathrm{~F}$\ Case II:- A wire of double the radius Breaking force $=\mathrm{F}_{2}$\ Area $=4 \mathrm{~A}$\ Breaking stress $=\frac{\mathrm{F}_{2}}{4 \mathrm{~A}}$\ From (1) \& (3) $\mathrm{F}_{2}=4 \mathrm{~F}$\ In short $\frac{F}{A}=\frac{F_{1}}{2 A}=\frac{F_{2}}{4 A}$\