1.

What will be the minimum diameter of a steel wire, which is used to raise a load of 4000N if the stress in the rod is not to exceed 95 MN/m2?

Answer»

ANSWER :

From the Question,

  • Force (F) = 4 × 10³ N

  • Stress = 95 MN/m² = 95 × 10^-3 N/m²

To finD

Diameter of the STEEL WIRE

Stress : Force acting per unit area of the object

\sf Stress = \dfrac{F}{A} \\ \\ \dashrightarrow \sf Stress = \dfrac{F}{\pi r^<klux>2</klux>}

Putting the values, we get :

\dashrightarrow \: \sf \: 95 \times {10}^{ - 2} = \dfrac{4 \times {10}^{3} }{3.14 \: \times {r}^{2} } \\ \\ \dashrightarrow \: \sf \: {r}^{2} = \dfrac{4 \times {10}^{5} }{3.14 \times 95} \\ \\ \dashrightarrow \: \sf \: r {}^{2} = \dfrac{4 \times {10}^{7} }{298.3} \\ \\ \dashrightarrow \: \sf \: {r}^{2} = 13.41 \\ \\ \dashrightarrow \: \boxed{ \boxed{ \sf r =3.66 \: m }}

WKT,

D = 2r = 2(3.66) = 7.32 m

Thus,the diameter of the steel wire should be atleast 7.32 m


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