Question

When a spring is extended by $2cm$ energy stored is $100J$. When extended by further $2cm$, the energy increases by

• A. $400J$
• B. $300J$
• C. $200J$
• D. $100J$

Answer 1

The correct option is B $300J$

When the spring is stretched by 2 cm :

$x=2$ cm $E=100$ J

Energy stored in spring $E=\frac{1}{2}k{x}^2$

$\therefore$ $100=\frac{1}{2}k(2{)}^2$ $⟹k=50$ $N/cm$

When the spring is further stretched by 2 cm :

Thus $x^{\prime }=2+2=4$ cm

Energy stored $E^{\prime }=\frac{1}{2}k(x^{\prime }{)}^2$

$\therefore$ $E^{\prime }=\frac{1}{2}\left(50\right)(4{)}^2=400$ J

Increase in energy $\Delta E=400-100=300$ J