Thailand · Grade 12 · Practice Sheet 48

1. 1.

   Two masses 7,000 kg and 220 kg are 17 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.

   In a triangle, a = 13, b = 13 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A triangle has sides a = 9 cm and b = 13 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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4. 4.

   A wave has frequency 138 Hz and wavelength 1.29 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A force of 210 N acts on an area of 9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the gravitational potential energy of a 18 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the force needed to accelerate a 58 kg mass at 3.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 493 N acts on an area of 9.9 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A current of 2.5 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Two masses 4,100 kg and 740 kg are 7 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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12. 12.

    In a triangle, a = 15, b = 8 and the included angle C = 80°. 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.

    A force of 20 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A device runs at 197 V drawing 4.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A current of 3.6 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A device runs at 111 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A wave has frequency 557 Hz and wavelength 2.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Two masses 3,000 kg and 690 kg are 4 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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20. 20.

    A 35 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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