Two springs of spring constant 1500 Nm - 1 and 3000 Nm -1 respectively are stretched with the same force. They will have potential energy in ratio

Question

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

Tardigrade Admin · Accepted Answer

The work done in pulling the string is stored as potential energy in the spring

U = \frac{1}{2} k x^{2} ... (i)

where

k

is spring constant and

x

is distance through which it is pulled.
Also in SHM
Force

\propto

displacement

F = k x ... (ii)

where

k

is spring constant
Putting

x = \frac{F}{k}

in Eq. (i), we get

U = \frac{1}{2} k (\frac{F}{2})^{2} = \frac{F ^{2}}{2 k}

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

∴ U_{1} : U_{2} = 2 : 1

Q. Two springs of spring constant $1500 N m^{- 1} an d 3000 N m^{- 1}$ respectively are stretched with the same force. They will have potential energy in ratio

1 : 2

2 : 1

1 : 4

4 : 1

Q. Two springs of spring constant 1500Nm−1and3000Nm−1 respectively are stretched with the same force. They will have potential energy in ratio

1 : 2

2 : 1

1 : 4

4 : 1

Q. Two springs of spring constant $1500 N m^{- 1} an d 3000 N m^{- 1}$ respectively are stretched with the same force. They will have potential energy in ratio