Related Questions

    1.

    The angular velocities of three bodies in simple harmonic motion are Ο‰1,  ω2,  ω3{\omega _1},\,\,{\omega _2},\,\,{\omega _3} with their respective amplitudes as A1,  A2,  A3,.{A_1},\,\,{A_2},\,\,{A_3},. If all the bodies have same mass and velocity, then

    A

    A1Ο‰1  =A2Ο‰2  =  A3Ο‰3{A_1}{\omega _1}\,\, = {A_2}{\omega _2}\,\, = \,\,{A_3}{\omega _3}

    B

    A1Ο‰12  =A2Ο‰22  =A3Ο‰32{A_1}\omega _1^2\,\, = {A_2}\omega _2^2\,\, = {A_3}\omega _3^2

    C

    A12Ο‰1=A22Ο‰2=A32Ο‰3A_1^2{\omega _1} = A_2^2{\omega _2} = A_3^2{\omega _3}

    D

    A12Ο‰12  =A22Ο‰22  =A2A_1^2\omega _1^2\,\, = A_2^2\omega _2^2\,\, = {A^2}

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    4.

    If a simple pendulum of length l has maximum angular displacement ΞΈ, then the maximum kinetic energy of bob of mass m is

    A

    12imes(lg)\frac{1}{2} imes \left( {\frac{{\rm{l}}}{{\rm{g}}}} \right)

    B

    12imesmgl\frac{1}{2} imes \frac{{{\rm{mg}}}}{{\rm{l}}}

    C

    mglimes(1βˆ’cos⁑heta)mgl imes (1 - \cos {\rm{heta )}}

    D

    12imesmglsin⁑heta\frac{1}{2} imes mgl\sin {\rm{heta }}

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    8.

    If a simple harmonic is represented by \frac{{{d^2}x}}{{d{t^2}}}$$ + \alpha x = 0,its time period is

    A

    2πα\frac{{2\pi }}{\alpha }

    B

    2πα\frac{{2\pi }}{{\sqrt \alpha }}

    C

    2πα2\pi \alpha

    D

    2πα2\pi \sqrt \alpha

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    10.

    A tunnel is made across the earth of radius RR, passing through its centre. A ball is dropped from a height h in the tunnel. The motion will be periodic with time period.

    A

    2Ο€Rg+4hg2\pi \sqrt {\frac{R}{g}} + 4\sqrt {\frac{h}{g}}

    B

    2Ο€Rg+42hg2\pi \sqrt {\frac{R}{g}} + 4\sqrt {\frac{{2h}}{g}}

    C

    2Ο€Rg+hg2\pi \sqrt {\frac{R}{g}} + \sqrt {\frac{h}{g}}

    D

    2Ο€Rg+2hg2\pi \sqrt {\frac{R}{g}} + \sqrt {\frac{{2h}}{g}}

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