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In a spring- mass system , the length of...

In a spring- mass system , the length of the spring is L, and it has a mass M attached to it and oscillates with an angular frequency `omega`. The spring is then cut into two parts, one (i) with relaxed length `alphaL` and the other (ii) with relaxed length `(1-alpha)` L. The force constants of the two spring A and B are

A

`(k)/(1-alpha)` and `(k)/(alpha)`

B

`(k)/(alpha)` and `(k)/(1-alpha)`

C

`alphak,(1-alpha)k`

D

k and k

Text Solution

Verified by Experts

The correct Answer is:
B
(b)Force constant , `k prop(1)/("Length of spring")`
`therefore (k_(A))/(k)=(L)/(alphaL)`
`therefore k_(A)=(k)/(alpha)`
Similarly, `k_(B)=(k)/(1-alpha)`
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