Sri Lanka · Grade 12 · Practice Sheet 11

1. 1.

   Two masses 2,700 kg and 550 kg are 19 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.

   Rs 800 is invested at 6% 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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3. 3.

   Find the sum of the first 8 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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4. 4.

   A force of 262 N acts on an area of 4.2 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A wave has frequency 201 Hz and wavelength 3.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 9 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the population standard deviation of: 15, 7, 3, 12, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A cone has base radius 7 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    Find the momentum of a 17 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A wave has frequency 59 Hz and wavelength 2.89 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A current of 7.8 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the population standard deviation of: 3, 9, 8, 12, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A population of 8,800 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    Find the force needed to accelerate a 44 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 214 N acts on an area of 4.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 14 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the momentum of a 59 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A wave has frequency 398 Hz and wavelength 3.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A population of 2,500 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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