A mechanical system constans 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 `Delta l` is

Options

A. `(1)/(2) ((k_(1) k_(2))/(k_(1) + k_(2))) Delta l^(2)`
B. `k_(1) k_(2) Delta l^(2)`
C. `((k_(1)k_(2))/(k_(1) + k_(2))) Delta l^(2)`
D. `((k_(1) k_(2))/(k_(1) + k_(2))) Delta l`

Answer

A

Explanation

`K_(eq)`(in series) `= (k_(1) k_(2))/(k_(1) + k_(2))`
Work done to stretch springs with elongation `Delta l` is
`W = (1)/(2) K_(eq) .Delta l^(2) = (1)/(2) ((k_(1)k_(2))/(k_(1) + k_(2))). Delta l^(2)`