Question

Two springs A and B are stretched by applying forces of equal magnitudes at the four ends. If spring constant of A is 2 times greater than that of spring constant of B, and the energy stored in A is E, then that in B is

Options

• E/2

• 2E

• E

• E/4

Answer 1

2E

Explanation:

Forces have the same magnitude.

∴ k_ax_a = k_bx_b 

as k_a = 2k_b 

x_a = `x_b/2`

∴ Ea = E = `1/2 k_a x_a^2`

i.e. E = `1/2(2k_b)((x_b)/2)^2`

∴ `E/E_b = (2k_b xx x_b^2/4)/(k_b xx x_b^2)`

∴ `E/E_b = 1/2`

∴ E_b = 2E