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:
1:6
1:9
1:11
1:14
As discussed in
Series combination of spring -
- wherein
are spring constants of spring 1 & 2 respectively.
and
Parallel combination of spring -
- wherein
are spring constants of spring 1 & 2 respectively.
Three strings of lengths with force constant
Connected in series
K' = K
When connected in paralllel
K" = 6K + 3K + 2K = 11K
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