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Jyoti Tarun Dayal
Asked: 2022-10-29T16:59:08+05:30 In:

A block of mass `m`, when attached to a uniform ideal apring with force constant `k` and free length `L` executes SHM. The spring is then cut in two pieces, one with free length n `L` and other with free length `(1 – n)L`. The block is also divided in the same fraction. The smaller part of the block attached to longer part of the spring executes SHM with frequency `f_(1)` . The bigger part of the block attached to smaller part of the spring executes SHM with frequency `f_(2)`. The ratio `f_(1)//f_(2)` is
A. `1`
B. `(n)/(1 – n)`
C. `(1 + n)/(n)`
D. `(n)/(1 + n)`

A block of mass `m`, when attached to a uniform ideal apring with force constant `k` and free length `L` executes SHM. The spring is then cut in two pieces, one with free length n `L` and other with free length `(1 – n)L`. The block is also divided in the same fraction. The smaller part of the block attached to longer part of the spring executes SHM with frequency `f_(1)` . The bigger part of the block attached to smaller part of the spring executes SHM with frequency `f_(2)`. The ratio `f_(1)//f_(2)` is
A. `1`
B. `(n)/(1 – n)`
C. `(1 + n)/(n)`
D. `(n)/(1 + n)`
Parabola
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1 Answer

  1. Correct Answer – A
    `k prop (1)/(“Length of spring”)`
    `{:(“Length”,”Force constant”),(L,k),(nL,k//n),((1-n),k//(1-n)):}`
    `m_(1) = nm`
    and `m_(2) = (1 – n)m`
    `(f_(1))/(f_(2)) = ((1)/(2pi)sqrt ((k//n)/((1 – n)m)))/((1)/(2pi)sqrt((k//(1 – n))/(nm))) = 1`

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