System of Particles and Rotational Motion

System of Particles and Rotational Motion

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System of Particles and Rotational Motion
  1. A fly wheel rotating about a fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is








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    Er =
    1
    		Iω²
    2

    I =
    2Er
    		 =
    2 × 360
    		 = 0.8 kgm²
    ω²30 × 30

    Correct Option: C

    Er =
    1
    		Iω²
    2

    I =
    2Er
    		 =
    2 × 360
    		 = 0.8 kgm²
    ω²30 × 30

  1. A composite disc is to be made using equal masses of aluminium and iron so that it has as high a moment of inertia as possible. This is possible when








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    Density of iron > density of aluminium

    ∴ Since, ρiron > ρaluminium
    So, whole of aluminium is kept in the core and the iron at the outer rim of the disc. 

    Correct Option: B

    Density of iron > density of aluminium

    ∴ Since, ρiron > ρaluminium
    So, whole of aluminium is kept in the core and the iron at the outer rim of the disc. 

  1. A thin uniform circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclination plane will be








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    a =
    g sinθ
    		 =
    g sin 30°
    		 =
    g
    1 + K²/R²1 + 14

    Correct Option: C

    a =
    g sinθ
    		 =
    g sin 30°
    		 =
    g
    1 + K²/R²1 + 14

  1. Angular momentum is








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    Angular momentum →L is defined as
    →L = r' × m(v')
    So, L' is  an axial vector.

    Correct Option: A

    Angular momentum →L is defined as
    →L = r' × m(v')
    So, L' is  an axial vector.

  1. The angular momentum of a body with mass (m), moment of inertia (I) and angular velocity (ω) rad/sec is equal to








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    Let body contain m1, m2, m3........mn masses at distance r1, r2, r3 ........ rn from axis OA.
    Angular momentum of body
    = m1v1r1 + m2v2r2 .....+ mnvnrn
    = m1(ωr1)r1 + m2(ωr2)r2 .......... + mn(ωrn)rn
    = (m1r1²)ω + (m2r2²)ω .......... + (mnrn²)ω

    Correct Option: A

    Let body contain m1, m2, m3........mn masses at distance r1, r2, r3 ........ rn from axis OA.
    Angular momentum of body
    = m1v1r1 + m2v2r2 .....+ mnvnrn
    = m1(ωr1)r1 + m2(ωr2)r2 .......... + mn(ωrn)rn
    = (m1r1²)ω + (m2r2²)ω .......... + (mnrn²)ω