Question

The given setup is in equilibrium. Springs were in natural length before the force was applied. If I have to replace the above setup of 1 block and 2 springs by 1 block and 1 spring, what will be the spring constant of that new spring such that the block is displaced by the same amount as previously?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

There is a force F on the block in rightward direction.

Because of it the spring on the left will elongate by x₀ and right will compress simultaneously by $x_0$

free body diagram

$\Rightarrow F=K_1{X}_0+K_2{X}_0$ ............(i)

Now if I replace 2 springs with just 1 & i get same displacement of block by $X_0$

F = KX ..............(ii)

(i) = (ii)

$(K_1+K_2)X_0=K{X}_0\Rightarrow K=K_1+K_2$