when a spring is divided into two parts in the ratio 1:2 does it mean if we take one to be spring constant to be k1 the other becomes 2k1?

Dear student,
Yes very correct k1 and 2k1 will be the spring constants...
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Askiitians Expert
Sagar Singh
B.Tech, IIT Delhi

no spring constant depends on nature of materials

k(spring constant) inversly proportional to l(length) ...

k¹/k = L/L¹ 

length of two parts are L/3 , 2L/3

comparing spring constant of each part with original we get

k₁  = 3k (spring constant of smaller part)

k₂ = 3k/2 (spring constant of larger part)

Sir u r wrong @sagar Because if a spring is cut in m:n .Then the resultant springs having stiffness (m+n)/n and (m+n)/m respectively .VSYMADE EASY

Spring constant is inversely proportional to length but from your formula it is directly proportional so please render changes in your formula The correct formula should be If spring is cut in ratio m:n then(m+n)/m and (m+n)/n