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JAMB Physics 2023 Paper

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Question : 16

Total: 65

A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire.

[Take g = 10 ms

^{-2}

]

$2.4 \times 10^{10} (\mathrm{Nm}^{-2})$
$1.5 \times 10^{10} (\mathrm{Nm}^{-2})$
$2.4 \times 10^{9} (\mathrm{Nm}^{-2})$
$1.3 \times 10^{10} (\mathrm{Nm}^{-2})$

Solution:

r=0.2mm = $2 \times 10^{-4}$ e= 0.05% of L,=0.005L, m=1.5kgg= $10 \mathrm{ms}^{-2}$ , y=?,

(1000 mm = 1m)

Y =

\frac{FL}{Ae}

w = mg = 1.5 × 10 = 15

A =

\pi r^2

=

\frac{22}{7} \times (2 \times 10^{-4})^2

=

1.26 \times 10^{-7} (\mathrm{m}^2)

⇒ Y =

\frac{15L}{1.26 \times 10^{-7} \times 0.005L}

⇒ Y = $\frac{15}{1.26 \times 10^{-7} \times 0.005}$

⇒ Y =

\frac{15}{6.29 \times 10^{-10}}

Y =

2.4 \times 10^{10} (\mathrm{Nm}^{-2})

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