A spring of relaxed length \ell_{1} and spring constant k_{1} is placed ‘in parallel’ with a spring of relaxed length \ell_{2} and spring constant k_{2}. A force F is applied to each end. The combination of the springs acts like a single spring with spring constant k and relaxed length \ell where
Answer Choices
A. k=k_{1}+k_{2} \quad and \quad \ell=\ell_{1} \ell_{2} /\left(\ell_{1}+\ell_{2}\right)
B. k=k_{1}+k_{2} \quad and \quad \ell=\left(\ell_{1} k_{1}+\ell_{2} k_{2}\right) /\left(k_{1}+k_{2}\right)
C. k=k_{1}+k_{2} \quad and \quad \ell=\left(\ell_{1} k_{2}+\ell_{2} k_{1}\right) /\left(k_{1}+k_{2}\right)
D. k=\left(\ell_{1} k_{1}+\ell_{2} k_{2}\right) /\left(\ell_{1}+\ell_{2}\right) \quad and \quad \ell=\left(\ell_{1} k_{1}+\ell_{2} k_{2}\right) /\left(k_{1}+k_{2}\right)
E. k=\left(\ell_{2} k_{1}+\ell_{1} k_{2}\right) /\left(\ell_{1}+\ell_{2}\right) \quad and \quad \ell=\left(\ell_{1} k_{2}+\ell_{2} k_{1}\right) /\left(k_{1}+k_{2}\right)
