Question

if stretch in a spring of force constant k is tripled then the ratio of elastic potential energy in the 2 cases will be
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Answer 1

Given:

Spring force constant = k

To find:

The ratio of the potential energy of the spring when the spring force constant is increased from k to 3k.

Solution:

As we know that the potential energy of a spring = 1/2 kx²

When the force constant of the spring is tripled, i.e. from k to 3k then the potential energy would be:

P.E = 1/2 (3k) x²

The ratio of both the potential energies:

= (1/2 * 3k * x²) / (1/2 * k * x²)

= 3/1

Therefore the ratio of elastic potential energy in the 2 cases will be 3/1.