Nepal · Class 11 · Practice Sheet 4

1. 1.

   Find the force needed to accelerate a 12 kg mass at 2.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A triangle has sides a = 15 cm and b = 9 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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3. 3.

   Two masses 4,300 kg and 230 kg are 9 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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4. 4.

   In a triangle, a = 12, b = 9 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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5. 5.

   A force of 5 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A force of 42 N acts on an area of 6.7 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the force needed to accelerate a 3 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the population standard deviation of: 6, 18, 17, 13, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A wave has frequency 423 Hz and wavelength 1.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Two masses 2,200 kg and 470 kg are 11 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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11. 11.

    An object with initial velocity 11 m/s accelerates at 2.9 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A population of 4,000 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A 39 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A current of 7.5 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A body starts at 2 m/s and accelerates at 1.6 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Solve using the quadratic formula: x² + 1x − 20 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    An object has mass 8.5 g and volume 5 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the population standard deviation of: 3, 4, 4, 15, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A force of 116 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Solve using the quadratic formula: x² − 7x + 6 = 0.

    Formula:Quadratic Formula

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

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