Two springs A and B , having spring constants related by k_A = 2k_B , are stretched using forces of equal magnitudes at the four ends. If spring A stores an energy E , the energy stored in spring B will be

Step-by-step solution

The energy stored in a spring stretched by a force F is given by U = 1 2 kx^2 . Since F = kx , the extension is x = F k . Substituting x in the energy expression, we get U = F^2 2k . Given that both springs are stretched by forces of equal magnitudes, F_A = F_B = F . For spring A , the stored energy is E = F^2 2k_A . For spring B , the stored energy is E_B = F^2 2k_B . Given k_A = 2k_B , we can write k_B = k_A 2 . Substituting this into the equation for E_B gives: E_B = F^2 2 ( k_A 2 ) = 2 ( F^2 2k_A ) = 2E .