United Kingdom · Year 12 · Practice Sheet 25

1. 1.

   Two masses 5,500 kg and 630 kg are 12 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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2. 2.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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3. 3.

   A population of 6,700 grows 5% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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4. 4.

   A force of 48 N acts on an area of 7.1 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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5. 5.

   Two masses 4,800 kg and 320 kg are 6 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   Find the momentum of a 34 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Solve using the quadratic formula: x² − 8x + 12 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   Find the force needed to accelerate a 41 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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10. 10.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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11. 11.

    A force of 118 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    In a triangle, a = 8, b = 16 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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13. 13.

    Find the force needed to accelerate a 37 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A 22 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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15. 15.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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16. 16.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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17. 17.

    A current of 5.4 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 426 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    Find the momentum of a 59 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A wave has frequency 65 Hz and wavelength 3.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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