Pakistan · Class 11 · Practice Sheet 47

1. 1.

   Find the momentum of a 30 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the population standard deviation of: 19, 15, 14, 3, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the force needed to accelerate a 25 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 9 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A body starts at 0 m/s and accelerates at 5.5 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the momentum of a 5 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A current of 1.4 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A force of 317 N acts on an area of 5.8 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A triangle has sides a = 10 cm and b = 12 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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10. 10.

    A wave has frequency 433 Hz and wavelength 2.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A 4 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Find the gravitational potential energy of a 26 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Solve using the quadratic formula: x² + 9x + 20 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A cylinder has radius 13 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Two masses 5,700 kg and 740 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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16. 16.

    An object with initial velocity 11 m/s accelerates at 2.1 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A wave has frequency 229 Hz and wavelength 4.37 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    An object with initial velocity 5 m/s accelerates at 4.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    Find the momentum of a 49 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    An object has mass 278.4 g and volume 48 cm³. Find its density.

    Formula:Density

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

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