Ireland · Year 11 · Practice Sheet 25

1. 1.

   Two masses 7,300 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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2. 2.

   A device runs at 15 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A cone has base radius 11 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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4. 4.

   Find the population standard deviation of: 14, 4, 7, 14, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 3 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A force of 16 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   An object with initial velocity 13 m/s accelerates at 1.9 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A force of 138 N acts on an area of 7.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A 39 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A force of 69 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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11. 11.

    €1,400 is invested at 3% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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12. 12.

    Find the gravitational potential energy of a 23 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    €1,600 is invested at 4% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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14. 14.

    Find the gravitational potential energy of a 27 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the population standard deviation of: 8, 16, 13, 12, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A force of 65 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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17. 17.

    Find the population standard deviation of: 10, 5, 4, 8, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Solve using the quadratic formula: x² + 5x − 6 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A current of 2.4 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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