Question

The two wires shown in figure are made of the same material which has a breaking stress of 8 × 10⁸ N m⁻². The area of cross section of the upper wire is 0.006 cm² and that of the lower wire is 0.003 cm². The mass m₁ = 10 kg, m₂ = 20 kg and the hanger is light.   Repeat the above part if m₁ = 10 kg and m₂ = 36 kg. 

Answer 1

\[\text{If m}_1 = 10 \text{ kg and m}_2 = 36 \text{ kg }\]

Tension in lower wire  \[ \text{T}_\text{l} = \text{m}_1 \text{ g + w} \]

Here: g is the acceleration due to gravity
           w is the load
∴ Stress in lower wire: 

\[\Rightarrow \frac{\text{T}_\text{l}}{\text{A}_\text{l}} = \frac{\text{m}_1\text{ g + w}}{\text{A}_\text{l}} = 8 \times {10}^5 \]
\[ \Rightarrow \text{ w = 140 N }\]

Now, tension in upper wire

\[\text{T}_2 = \text{m}_1 \text{ g + m}_2 \text{ g + w }\]

∴ Stress in upper wire:

\[\Rightarrow \frac{\text{T}_\text{u}}{\text{A}_\text{u}} = \frac{\text{m}_2 \text{g + m}_1 \text{g + w}}{\text{A}_\text{u}} = 8 \times {10}^5 \]
\[ \Rightarrow \text{w = 20 N}\]

For the same breaking stress, the maximum load that can be put is 20 N or 2 kg. The upper wire will break first if the load is increased.