Nepal · Class 12 · Practice Sheet 43

1. 1.

   Find the population standard deviation of: 18, 7, 18, 17, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the momentum of a 14 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 171 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A 18 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A cone has base radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Two masses 6,200 kg and 140 kg are 10 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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7. 7.

   A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   Find the force needed to accelerate a 60 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 3 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the population standard deviation of: 12, 5, 20, 15, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A force of 91 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    An object with initial velocity 4 m/s accelerates at 1.6 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    A body starts at 7 m/s and accelerates at 1.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Two masses 2,100 kg and 390 kg are 12 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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15. 15.

    A force of 64 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the population standard deviation of: 9, 11, 8, 16, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A population of 5,300 grows 2% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the momentum of a 41 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    An object with initial velocity 4 m/s accelerates at 4.7 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the force needed to accelerate a 41 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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