Question

Identical springs of steel and copper $(Y_{steel}>Y_{copper})$ are equally stretched then:

• A. Less work is done on copper spring
• B. Less work is done on steel spring
• C. Equal work is done on both the springs
• D. Data is incomplete

Answer 1

Answer: (B)

Less work is done on steel spring

Work done, $W=\frac{1}{2}\times F\times \Delta L$
For a given $F$
$W\propto \Delta L...\left(i\right)$
and $\Delta L=\frac{FL}{AY}$
As $F,A$ and $L$ are constants
$\therefore \Delta L\propto \frac{1}{Y}...\left(ii\right)$
From (i) and (ii), we get
$W\propto \frac{1}{Y}$
$\therefore \frac{W_{steel}}{W_{copper}}=\frac{Y_{copper}}{Y_{steel}}$

As $Y_{copper}<Y_{steel}$
$\therefore W_{steel}<W_{copper}$
So, less work is done on steel spring