Question

HI Friends !!
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?

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Answer 1

Aɴꜱᴡᴇʀ

$\large{\green{\sf{ \: Diameter \: of \: Steel \: wire \: required = \: 7.32 \: mm}}}$

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Gɪᴠᴇɴ

Force = 4000 N

Stress = 95 MN/m² = $\tt{95 \: Nmm^{-2}}$

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ᴛᴏ ꜰɪɴᴅ

Minimum Diameter of the Steel Wire

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Sᴛᴇᴘꜱ

As we already know,

$\begin{lgathered}\large{\orange{\sf{Stress \: = \: \dfrac{Force}{Area}}}} \\ \\ \leadsto {\tt{Stress \: = \: \dfrac{Force}{\pi r^2}}} \\ \\ \leadsto \tt{95 \: = \: \dfrac{4000}{\pi r^2}} \\ \\ \leadsto\tt{r^2 \: = \: \dfrac{4000}{95 \: \times \: 3.14}} \\ \\ \leadsto \tt{r^2 \: = \: \dfrac{4000}{298.3}} \\ \\ \leadsto\tt{r^2 \: = \: 13.4} \\ \\ \leadsto\tt{r \: = \: \sqrt{13.4}} \\ \\ \leadsto \tt{r \: = \: 3.66} \\ \\ \pink{\dashrightarrow{\sf{ \: Radius \: of \: steel \: wire \: is \: 3.66 \: mm}}}\end{lgathered}$

Then,

$\begin{lgathered}\leadsto \tt{Diameter \: = \: 2 \: \times \: Radius} \\ \\ \leadsto \tt{Diameter \: = \: 3.66 \: \times \: 2} \\ \\ \leadsto \tt{Diameter \: = \: 7.32} \\ \\ \pink{\dashrightarrow{\sf{ \: Diameter \: of \: Steel \: wire \: required \: is \: 7.32 \: mm}}}\end{lgathered}$

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$

Answer 2

hello da

ur answer ...

i hope that this may help u da

try to make my answer as brainaliest