Poland · Klasa 12 · Practice Sheet 46

1. 1.

   Two masses 2,800 kg and 680 kg are 3 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.

   A cone has base radius 6 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   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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4. 4.

   Find the momentum of a 25 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A wave has frequency 37 Hz and wavelength 1.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the momentum of a 31 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 442 N acts on an area of 5.3 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A 35 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the force needed to accelerate a 42 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 55 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the momentum of a 49 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A device runs at 137 V drawing 2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A current of 1 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A force of 35 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the sum of the first 4 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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16. 16.

    Find the force needed to accelerate a 38 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A triangle has sides a = 12 cm and b = 19 cm with an included angle C = 60°. 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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19. 19.

    A device runs at 136 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A current of 1.8 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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