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One end of a light spring constant k and...

One end of a light spring constant `k` and natural length `l_(0)` is fixed and the other end is attached to a block of mass `m` lying on smooth horizontal surface. If the block is rotating in the horizontal circle of radius `l`, find the frequency of the revolution.

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Extension of spring `x=l-l_(0)`
Here, the necessary centripetal force is provide by the spring force `kx`
`kx=momega^(2)l`
`k(l-l_(0)=m omega^(2)l`
`omega=sqrt((k(l-l_(0)))/(ml))`
`2pif=sqrt((k(l-l_(0)))/(ml))`
`f=(1)/(2pi)sqrt((k(l-l_(0)))/(ml))`
where `f` is the frequency of revolution.
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Knowledge Check

  • One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacment, the work done by the spring is +(1/2)kx^(2) . The possible cases are.

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    The spring was initially compessed by a distance x and was finally in its natural length .
    B
    It was initially stretched by a distance x and finally was in its natural length.
    C
    It was initially natural length and finally in a compressed position.
    D
    It was initially in its natural length and finally in a stretched position.

  • One end of aspring of force constant k is fixed to a verticle wall and the other to a block of mass m resing on a smooth horizontal surface There is another and wall at a distance x_(0) from the block The spring is then compressed by 2x_(0) and released The time taken to at the wall is

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    `(1)/(6)pi sqrt((k)/(m))`
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  • A rotor is rotating with a constant angular velocity omega about its own axis. At the centre of the rotaor a spring is fixed of natural length (l_(0)) whose other end is connected to a block of mass m. Find the minimum vaule of coefficient of friction between block and rotor wall for which spring remains horizontal. The radius of rotor is R (R lt l_(0)) .

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    D
    `mu = (mg)/(KR)`

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