Ncert Exercises & Solutions

Young's modulus of steel is $1.9 \times 10^{11} ~\text{N/m}^2$. When expressed in CGS units of $\text{dyne/cm}^2$, it will be equal to: $(1 \mathrm{~N}=10^5 \text { dyne, } 1~ \text{m}^2=10^4 ~\text{cm}^2)$
1. $ 1.9 \times 10^{10} $
2. $ 1.9 \times 10^{11} $
3. $ 1.9 \times 10^{12} $
4. $ 1.9 \times 10^9$

(3) Hint: Use the concept of conversion of units.

$Step 1 : Convert Newton into dyne .$
$\begin{array}{ll} Given, Young's modulus, Y = 1 .9 \times 10^{11} N / m^{2} \\ 1 N = 10^{5} dyne \\ Hence, Y = 1 .9 \times 10^{11} \times 10^{5} dyne / m^{2} \\ Step 2 : Convert metre into centimetre . \end{array}$
$\begin{array}{lrl} We know that \begin{aligned} 1 m & = 100 cm \end{aligned} \\ ∴ = 1 .9 \times 10^{11} \times 10^{5} dyne / (100)^{2} {cm}^{2} \\ = 1 .9 \times 10^{16 - 4} dyne / {cm}^{2} \\ = 1 .9 \times 10^{12} dyne / {cm}^{2} \end{array}$

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