Centres of mass of rigid bodies

Centres of mass of rigid bodies Quiz

Spec 3.1 · Edexcel A-Level Further Maths: Quiz

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  1. 1. A uniform solid cone has height 12 cm. How far is its centre of mass from its base?

    • A. 33 cm
    • B. 44 cm
    • C. 66 cm
    • D. 99 cm

  2. 2. A uniform solid hemisphere has radius 8 cm. How far is its centre of mass from its plane face?

    • A. 44 cm
    • B. 33 cm
    • C. 3.403.40 cm
    • D. 66 cm

  3. 3. The region under y=x2y=x^2 for 0≤x≤20\le x\le2 is rotated about the xx-axis. What is the volume of the solid?

    • A. 8π3\frac{8\pi}{3}
    • B. 64π5\frac{64\pi}{5}
    • C. 32π5\frac{32\pi}{5}
    • D. 16π3\frac{16\pi}{3}

  4. 4. A rod of length 3 m has mass per unit length 2x2x kg m⁻¹ at distance xx from one end. How far is the centre of mass from that end?

    • A. 1.51.5 m
    • B. 2.252.25 m
    • C. 1.81.8 m
    • D. 22 m

  5. 5. A uniform solid is formed by rotating y=f(x)y=f(x) about the xx-axis. Which expression gives xˉ\bar x?

    • A. ∫xy dx∫y dx\frac{\int xy\,dx}{\int y\,dx}
    • B. ∫xy2 dx∫y2 dx\frac{\int xy^2\,dx}{\int y^2\,dx}
    • C. ∫y2 dx2∫y dx\frac{\int y^2\,dx}{2\int y\,dx}
    • D. ∫x2y dx∫y dx\frac{\int x^2y\,dx}{\int y\,dx}

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