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A spring is connected to a mass m suspen...

A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. spring is now cut into two equal halved and the same mass is suspended fron one of the havles. The period of vertical oscillation is :

A

`T'=sqrt(2)T`

B

`T'=(T)/(sqrt(2))`

C

`T'=sqrt(2T)`

D

`T'=sqrt((T)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Spring constant of spring depends upon number of coil in the spring. When you cut the spring then the number of coil remain half of the original, so
`k.=2k`
Time period of the spring, `T=2pisqrt((m)/(k))`
If the spring is halves, So the time period
`T.=2pisqrt((m)/(k.))=2pisqrt((m)/(2k))`
`T.=(1)/(sqrt(2))xx2pisqrt((m)/(k))impliesT.=(T)/(sqrt(2))`
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Knowledge Check

  • A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is

    A
    `T'=sqrt2 T`
    B
    `T'=(T)/(sqrt2)`
    C
    `T'=sqrt(2T)`
    D
    `T'=sqrt(T/2)`

  • A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. The spring is now cut into two equal halves and the same mass is suspended from one of the halves . The period of vertical oscillation is

    A
    `T'=sqrt(2)T`
    B
    `T'=(T)/(sqrt(2))`
    C
    `T'=sqrt(2T)`
    D
    `T'=sqrt((T)/(2))`

  • A massless spring, having force constant k, oscillates with a frequency n when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is suspended from one of the parts. The frequency of oscillation will now be………….

    A
    n
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    `nsqrt(2)`
    C
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