Question

Natural length of a spring is $60 \,cm$ and its spring constant is $4000 \,N / m$. A mass of $20\, kg$ is hung from it. The extension produced in the spring is $\left(\right.$ take $\left.g=9.8 \,m / s ^{2}\right)$ :

• A. 4.9 cm
• B. 0.49 cm
• C. 9.4 cm
• D. 0.94 cm

Answer 1

Answer: (A)

Given, $1=60 \,cm =60 \times 10^{-2}\, m$
$m =20\, kg ,$
$ k =4000\, N / m$
The weight hung from the spring
$= mg =20 \times 9.8=196\, N$
Let $x$ be the extension produced in spring.
Now, force applied by the spring $=$ downward force on the spring
$\therefore kx = mg $
$\Rightarrow x =\frac{ mg }{ k }$
or, $x=\frac{20 \times 9.8}{4000}$
$=0.049 \,m =4.9\, cm$