A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k. Then they are connected in parallel and force constant is k . Then k' : k" is:

  • Option 1)

    1:6

  • Option 2)

    1:9

  • Option 3)

    1:11

  • Option 4)

    1:14

 

Answers (1)

As discussed in

Series combination of spring -

- wherein

frac{1}{K_{eq}}= frac{1}{K_{1}}+ frac{1}{K_{2}}

K_{1}and K_{2} are spring constants of spring 1 & 2 respectively.

 

 and

Parallel combination of spring -

- wherein

K_{eq}=K_{1}+K_{2}

K_{1}and K_{2} are spring constants of spring 1 & 2 respectively.

 

Three strings of lengths \frac{l}{6}\:,\:\frac{2l}{6},\:and\:\frac{3l}{6}    with force constant

K_{1}= \frac{Kl}{\frac{l}{6}}= 6K

K_{2}= \frac{Kl}{\frac{2l}{6}}= 3K

K_{3}= \frac{Kl}{\frac{3l}{6}}= 2K

Connected in series

\frac{l}{K'}= \frac{1}{6K}+ \frac{1}{3K}+ \frac{1}{2K} = \frac{1+2+3}{6K}= \frac{1}{K}

K' = K

When connected in paralllel

K" = 6K + 3K + 2K = 11K

\frac{K'}{K"}= \frac{K}{11K}= \frac{1}{11}


Option 1)

1:6

This option is incorrect

Option 2)

1:9

This option is incorrect

Option 3)

1:11

This option is correct

Option 4)

1:14

This option is incorrect