Question 274: Properties of Matter

Question

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $$	imes$$ 10$$^{-6}$$ m. [Young's modulus for steel = 2 $$	imes$$ 10$$^{11}$$ Nm$$^{-2}$$ and g = 10 ms$$^{-2}$$ ]

Accepted Answer

$\begin{aligned} & r_1 =r_2=0.2 \mathrm{~cm}=2 	imes 10^{-3} \mathrm{~m} \\ & y_1 	ext { (steel) }  =2 	imes 10^{11} \mathrm{~N} \mathrm{~m}^{-2} \\ & l_1  =1.6 \mathrm{~m}\end{aligned}$
At equilibrium,
$$
\begin{aligned}
&T_2  =1.14 \mathrm{~g}=11.4 \mathrm{~N} \\
&T_2+2 g  =T_1 \\
&	herefore T_1 =11.4+20=31.4 \mathrm{~N}
\end{aligned}
$$
$$
\begin{aligned}
& \Delta l_1=\frac{T_1 l_1}{Y_1 A_1} \\
= & \frac{31.4 	imes 1.6}{2 	imes 10^{11} 	imes \pi\left(2 	imes 10^{-3}ight)^2} 1.1 \\
= & \frac{16}{8} 	imes 10^{-5} \\
= & 2 	imes 10^{-5} \mathrm{~m}=20 	imes 10^{-6} \mathrm{~m}
\end{aligned}
$$

Properties of Matter

Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is __________ $\times 10^{-6} m. [Young's modulus for steel = 2 \times 10^{11} Nm^{-2} and g = 10 ms^{-2}$ ]

Integer / Numeric Answer Type