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Q)

A spring 40 mm long is streched by application of a force. If 10 N force is required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is

\[(a)\;84\;J \quad (b)\;68 \;J\quad (c)\; 23\;J \quad (d)\;8\;J\]

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A)
Since 10 N force is required to stretch through 1 mm
$k=\large\frac{Force}{extension}$
$\quad=\large\frac{10}{10^{-3}}$
$k=10^4\;N/m$
$E=\large\frac{1}{2}$$kx^2$
$\quad=\large\frac{1}{2} $$\times 10^4 \times (40 \times 10^{-3})^2$
$\quad = 8\;J$
Hence d is the correct answer. 

 

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