Discussion Forum



1)

 A mechanical system consists two springs of stiffness coefficients $k_{1}$ and $k_{2}$  are connected in series . The minimum work to be  performed on the system to stretch it by $\triangle l$ is 


A) $\frac{1}{2}\left(\frac{k_{1}k_{2}}{k_{1}+k_{2}}\right) \triangle l^{2}$

B) $k_{1}k_{2} \triangle l^{2}$

C) $\left(\frac{k_{1}k_{2}}{k_{1}+k_{2}}\right) \triangle l^{2}$

D) $\left(\frac{k_{1}k_{2}}{k_{1}+k_{2}}\right) \triangle l^{}$

Answer:

Option A

Explanation:

 $K_{eq}$(in setries) = $\frac{k_{1}k_{2}}{k_{1}+k_{2}}$

 work done  to stretch  springs with elongation $\triangle l$ is 

$W= \frac{1}{2}K_{eq}.\triangle l^{2}=\frac{1}{2}\left(\frac{k_{1}k_{2}}{k_{1}+k_{2}}\right).\triangle l^{2}$