The potential energy stored in a spring is U when it is stretched for length 10 cm. If the spring is stretched for the next 10 cm then the change in its potential energy is equal to the:

CONCEPT:

Elastic potential energy:

• Elastic Potential Energy is the potential energy stored in an elastic material when it is stretched or compressed.
• When a spring is stretched by length 'x', potential energy stored in it is given by:

\(⇒ U=\frac{1}{2}kx^2\)

Where k is a spring constant and x is the displacement from the mean position.

CALCULATION:

• The potential energy stored in the spring when it is stretched for length 10 cm is given as, (x = 10 cm = 0.1 m)

\(⇒ U=\frac{1}{2}kx^2\)

\(⇒ U=\frac{1}{2}k\times0.1^2\)     -----(1)

• The potential energy stored in the spring when it is stretched for length 10 cm is given as, (x = 20 cm = 0.2 m)

\(⇒ U'=\frac{1}{2}kx^2\)

\(⇒ U'=\frac{1}{2}k\times0.2^2\)     -----(2)

By equation 1 and equation 2,

⇒ U' = 4U     -----(3)

• So the change in potential energy is given as,

⇒ ΔU = U' - U

⇒ ΔU = 4U - U

⇒ ΔU = 3U

• Hence, option 1 is correct.