Question

A spring of force constant $800N/m$ has an extension of $5cm$. The work done in extending it from $5cm$ to $15cm$ is :

• A. $16J$
• B. $8J$
• C. $32J$
• D. $24J$

Answer 1

Answer: (B)

$8J$

The work done is stored as elastic potential energy in the spring.

It is given by

$W=\frac{1}{2}\times k(x_2^2-x_1^2)$

$x_1=5cm$

$x_2=15cm$

Force constant, $k=800N/m=\frac{800}{100}N/cm=8N/cm$

$W=\frac{1}{2}\times 8({15}^2-5^2)=\frac{1}{2}\times 8(225-25)$

$=\frac{1}{2}\times 8\times 200=800Ncm$

$W=800Ncm=8Nm=8J$

Therefore,

The work done in extending it from $5cm$ to $15cm$ is $8J$.