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A uniform spring whose unstretched lengt...

A uniform spring whose unstretched length is l has a force constant k. the spring is cut into two pieces of unstretched lengths `l_(1)` and `l_(2)`, where `l_(1)=nl_(2)` and n is an integer. What are the corresponding force constant `k_(1)` and `k_(2)` in terms of n and k? what is the ratio `k_(1)//k_(2)`

A

`k eta and k(eta +1)`

B

`(k(eta+1))/(eta) and k(eta-1)`

C

`(k(eta-1))/(eta) and k(eta+1)`

D

`(k(eta+1))/(eta) and k(eta+1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`l_(1) = eta l_(2) rArr l_(1) : l_(2)=eta :1`
`rArr l_(1)=(eta)/(eta+1) l & l_(2)=(1)/((eta+1))l`
so `k_(1)=(eta+1)/(eta) k, k_(2)= (eta+1)k`
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