Australia · Year 11 · Practice Sheet 50

1. 1.

   An object has mass 51.3 g and volume 19 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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2. 2.

   Find the gravitational potential energy of a 33 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   $2,200 is invested at 8% compound interest per annum for 5 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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4. 4.

   A body starts at 18 m/s and accelerates at 3.6 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Two masses 1,100 kg and 180 kg are 8 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 sum of the first 9 terms of an arithmetic series with first term a = 8 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   Two masses 2,300 kg and 720 kg are 13 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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8. 8.

   A population of 6,800 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A force of 116 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A cone has base radius 9 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A right-angled triangle has legs of 9 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 12 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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13. 13.

    A wave has frequency 186 Hz and wavelength 3.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    $1,000 is invested at 6% compound interest per annum for 5 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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15. 15.

    A force of 455 N acts on an area of 6.3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A right-angled triangle has legs of 19 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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17. 17.

    Find the force needed to accelerate a 35 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 357 N acts on an area of 2.5 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the momentum of a 45 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A current of 6.6 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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