Spring question

Question

If a spring extends by x on loading then energy stored by the spring is :- ( T is tension in the spring, K = spring constant)

(A) T²/2x.                    (B) T²/2K

(C) 2K/T³                    (D) 2T²/K

Answer 1

Correct option is (A) \(\frac{T^2}{2k}\) 

If a spring with spring constant k is expanded or compressed by length x, then energy stored in spring is,

\(E=\frac{1}{2}kx^2\)

Step 1: Find relation between Spring Force and Tension.

It is given that spring is extended by length x. If spring constatnt is k then Tension in spring T is given as,

T = kx

⇒ x = T/k .....eq.1

Step 2: Find Energy stored in the spring.

Energy stored in the spring is given as,

\(E=\frac{1}{2}kx^2\)

⇒ \(E=k\frac{T^2}{2K^2}\) (By using eq.1)

⇒ \(E=\frac{T^2}{2K}\)

Thus, Energy stored in spring is given as, 

\(E =\frac{T^2}{2k}\)