Question

K is the force constant of a spring. The work done in increasing its extension from $l _ { 1 }$ to $l _ { 2 }$ will be

• A. $K \left( l _ { 2 } - l _ { 1 } \right)$
• B. $\frac { K } { 2 } \left( l _ { 2 } + l _ { 1 } \right)$
• C. $K \left( l _ { 2 } ^ { 2 } - l _ { 1 } ^ { 2 } \right)$
• D. $\frac { K } { 2 } \left( l _ { 2 } ^ { 2 } - l _ { 1 } ^ { 2 } \right)$

Answer 1

Answer: (D)

$\frac { K } { 2 } \left( l _ { 2 } ^ { 2 } - l _ { 1 } ^ { 2 } \right)$

Answer 2

At extension $l _ { 1 }$, the stored energy $= \frac { 1 } { 2 } K l _ { 1 } ^ { 2 }$

At extension $l _ { 2 }$, the stored energy$= \frac { 1 } { 2 } K l _ { 2 } ^ { 2 }$

Work done in increasing its extension from $l _ { 1 }$ to $l _ { 2 }$

$= \frac { 1 } { 2 } K \left( l _ { 2 } ^ { 2 } - l _ { 1 } ^ { 2 } \right)$