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A rod of mass M and length K is hinged a...

A rod of mass M and length K is hinged at its one end n carries a block f mass m at its other end. A spring of force constant `k_(1)` is installed at distance a form the hinge and another of force constant `k_(2)` at a distance b as shown in the figure. If the whole arrangement rests on a smooth horizontal table top. Find the frequency of vibrations.

A

`(1)/(2pi)sqrt((k_(1)a^(2)+k_(2)b^(2))/(L^(2)(m+(M)/(3))))`

B

`(1)/(2pi)sqrt((k_(1)a^(2)+k_(2)b^(2))/(L^(2)(m-(M)/(3))))`

C

`(1)/(2pi)sqrt((k_(1)a^(2)-k_(2)b^(2))/(L^(2)(m+(M)/(3))))`

D

`(1)/(4pi)sqrt((k_(1)a^(2)+k_(2)b^(2))/(L^(2)(m-(M)/(3))))`

Text Solution

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The correct Answer is:
A
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A rod of mass M and length K is hinged at its one end n carris a block f mass m at its other end. A spring of force constant k_(1) is installed at distance a form the hinge and another of force constant k_(2) at a distance b as shown in the figure. If the whole arrangement rests on a smoth horizontal table top. Find the frequency of vibrations.

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Knowledge Check

  • A rod of mass M and length L is hinged at its one end and carries a particle of mass m at its lower end. A spring of force constant k_(1) is installed at distance a from the hinge and another of force constant k_(2) at B distance b as shown in the figure. If the whcich arrangement rests on a smoth horizontal table top, the frequency of vibration is :

    A
    `(1)/(2pi)sqrt((k_(1)a^(2)+k_(2)b^(2))/(L^(2)(m + (M)/(3))))`
    B
    `(1)/(2pi)sqrt((k_(2)+k_(1))/(M+m))`
    C
    `(1)/(2pi)sqrt((k_(2)+k_(1)(a_(2))/(b^(2)))/(4(M)/(3)+m))`
    D
    `(1)/(2pi)sqrt((k_(1)+(k_(2)b_(2))/(a^(2)))/((4)/(3)m+M))`

  • A rod of mass M and length L is hinged at its one end and carries a particle of mass m at its lower end. A spring of force constant k_(1) is installed at distance a from the hinge and another of force constant k_(2) at B distance b as shown in the figure. If the whcich arrangement rests on a smoth horizontal table top, the frequency of vibration is :

    A
    `(1)/(2pi)sqrt((k_(1)a^(2)+k_(2)b^(2))/(L^(2)(m + (M)/(3))))`
    B
    `(1)/(2pi)sqrt((k_(2)+k_(1))/(M+m))`
    C
    `(1)/(2pi)sqrt((k_(2)+k_(1)(a_(2))/(b^(2)))/(4(M)/(3)+m))`
    D
    `(1)/(2pi)sqrt((k_(1)+(k_(2)b_(2))/(a^(2)))/((4)/(3)m+M))`

  • A rod of mass m and length l is hinged at 'its' end and released from rest in position shown. Find the force exerted by the hinge when the rod becomes horizontal

    A
    `(mg)/4`
    B
    `(3mg)/2 cos theta`
    C
    `(mg)/4sqrt(9cos^(2)theta+1/4)`
    D
    `(mg)/2 sqrt(9 cos^(2)theta+1/4)`

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