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Find the centre of mass of the disc shown in figure. . A square is removed from the disc as shown

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Knowledge Check

  • A disc of a mass M and radius R can rotate freely in vertical plane about a horizontal axis at O . Distant r from the centre of disc as shown in the figure. The disc is released from rest in the shown position. The angular acceleration of disc when OC rotates by an angles of 37^(@) is

    A
    `(8rg)/(5[R^(2)+2r^(2)])`
    B
    `(5rg)/(4[R^(2)+2r^(2)])`
    C
    `(10rg)/(3[R^(2)+2r^(2)])`
    D
    `(8rg)/(5R^(2))`

  • A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance r from the centre of the disc as shown in Fig. The disc is released from rest in the shown position. Answer the following questions based on the above information The angular velocity of the disc in the above described case is

    A
    `sqrt((8gr)/(5{R^(2)+2r^(2)]))`
    B
    `sqrt((6gr)/(5[R^(2)+2r^(2)]))`
    C
    `sqrt((12gr)/(5[R^(2)+2r^(2)]))`
    D
    `sqrt((12gr)/(5R^(2)))`

  • A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance r from the centre of the disc as shown in Fig. The disc is released from rest in the shown position. Answer the following questions based on the above information Reaction force exerted by the hinge on the disc at this instant is

    A
    `(Mg)/(5(R^(2)+2r^(2)))xxsqrt(9(R^(2)+6r^(2))^(2)+(4R^(2))^(2))`
    B
    `(Mg)/(5(R^(2)+2r^(2)))xx3(R^(2)+6r^(2))`
    C
    `(4Mg)/(5(R^(2)+2r^(2)))xxR^(2)`
    D
    `(Mg)/(5(R^(2)+2r^(2)))xx4R^(2)`

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