Ethiopia · Grade 12 · Practice Sheet 43

1. 1.

   Find the gravitational potential energy of a 23 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Two masses 2,700 kg and 490 kg are 10 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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3. 3.

   Find the force needed to accelerate a 10 kg mass at 5.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A 5 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A current of 6.1 A flows through a 36 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   An object with initial velocity 1 m/s accelerates at 1.6 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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7. 7.

   Find the momentum of a 25 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A cone has base radius 3 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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9. 9.

   A force of 68 N moves an object 24 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A triangle has sides a = 12 cm and b = 16 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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11. 11.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Find the force needed to accelerate a 29 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A population of 5,200 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    Find the momentum of a 51 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the gravitational potential energy of a 27 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the population standard deviation of: 8, 20, 6, 20, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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17. 17.

    An object with initial velocity 10 m/s accelerates at 4.9 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    A body starts at 20 m/s and accelerates at 2 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    In a triangle, a = 10, b = 15 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Two masses 7,900 kg and 220 kg are 15 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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