Question

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 constantis k''. Then k' : k'' is(a) 1 : 9(b) 1 : 11(c) 1 : 14(d) 1 : 6

Answer 1

Answer:

1:11

Explanation:

Force constant of spring = K ( Given)

Thus,

k∞1/Length

After cutting the spring in the ratio 1:2:3, the force constants will be in the ratio 6:3:2  which means K1 = 6k k2 = 3k K3 = 2k

 Force constant in series K will be given as -

1/K' = 1/6K+1/3K+1/2K

= 1/K'= 6/6K

= K' = K

Force constant in parallel K" : 6k+3k+2k = 11k

Hence K' / K" = 1 / 11

The said ratio will be 1:11