Question

the breaking stress of a wire is 7.2 × 10^8 Nm-2 and density 78 × 10^2 kg/m3 The wire is held vertically to the rigid support. the maximum length so the wire does not break is​

Answer 1

Given :

Breaking stress of a wire = 7.2 × 10⁸ N/m²

Density = 78 × 10^2 kg/m³

To find :

The maximum length so the wire does not break

Solution :

The maximum stress in the wire after which the wire begins to flow and breaks is called breaking stress.

Breaking stress = lρg

where,

l is the length of the given wire and ρ is it's material density.

By substituting all the given values in the formula,

$\dashrightarrow \sf B.S = l\rho g$

$\dashrightarrow \sf 7.2 \times {10}^{8} = l \times 78 \times {10}^{2} \times 10$

$\dashrightarrow \sf l = \dfrac{7.2 \times {10}^{8} \times 10 }{78 \times {10}^{2} }$

$\dashrightarrow \sf l = \dfrac{12 } {13} \times {10}^{4}$

$\dashrightarrow \sf l = 0.94 \times {10}^{4} m$

$\dashrightarrow \underline{\boxed{ \sf l = 9.4 \times {10}^{3} m}}$

Thus, the maximum length is 9.4 × 10³m.