Two springs of spring constant 1500 N / m and 3000 N / m respectively are stretched with the same force. They will have the potential energies in the ratio of :

Question

Two springs of spring constant 1500 N / m and 3000 N / m respectively are stretched with the same force. They will have the potential energies in the ratio of : (A) 1: 2 (B) 1: 4 (C) 4: 1 (D) 2: 1

Tardigrade Admin · Accepted Answer

When a body oscillates in simple harmonic. motion, it is acted upon by a restoring force which tends to bring it in the equilibrium position. Due to this force there is potential energy in the body.

Restoring force acting on body is

F =

mass

\times

acceleration

= m ω^{2} x

where,

ω

is angular frequency and

x

is displacement.
The work done in displacing the body appears as potential energy

U

.

U = W = 0 \int α m ω^{2} x d x = m ω^{2} \frac{x ^{2}}{2}

Here,

m ω^{2} = k =

spring constant.

∴ U_{1} = \frac{1}{2} k_{1} x^{2},

U_{2} = \frac{1}{2} k_{2} x^{2}

∴ \frac{U _{1}}{U _{2}} = \frac{1500}{3000} = \frac{1}{2}

∴ U_{1} : U_{2} = 1 : 2

Q. Two springs of spring constant $1500 N / m$ and $3000 N / m$ respectively are stretched with the same force. They will have the potential energies in the ratio of :

1 : 2

1 : 4

4 : 1

2 : 1

Q. Two springs of spring constant 1500N/m and 3000N/m respectively are stretched with the same force. They will have the potential energies in the ratio of :

1 : 2

1 : 4

4 : 1

2 : 1

Q. Two springs of spring constant $1500 N / m$ and $3000 N / m$ respectively are stretched with the same force. They will have the potential energies in the ratio of :