Question

A spring of spring constant $5\times {10}^{3}N/m$ is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

• A. 6.25 N-m
• B. 12.50 N-m
• C. 18.75 N-m
• D. 25.00N-m

Answer 1

The correct option is C

18.75 N-m

Work done to stretch the spring from $x_{1}to{x}_2$

$W=\frac{1}{2}k(x_2^2-x_1^2)=\frac{1}{2}5\times {10}^3\left[\right(10\times {10}^{-2}{)}^2-(5\times {10}^{-2}{)}^2]=\frac{1}{2}\times 5\times {10}^3\times 75\times {10}^{-4}=18.75Nm.$