Bangladesh · Class 11 · Practice Sheet 22

1. 1.

   Find the momentum of a 4 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Two masses 1,700 kg and 900 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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3. 3.

   Find the force needed to accelerate a 55 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the population standard deviation of: 16, 9, 6, 18, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the sum of the first 7 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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6. 6.

   Find the population standard deviation of: 11, 10, 18, 12, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   ৳ 3,600 is invested at 5% 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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9. 9.

   A triangle has sides a = 7 cm and b = 18 cm with an included angle C = 120°. 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.

    An object has mass 69.3 g and volume 21 cm³. Find its density.

    Formula:Density

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

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11. 11.

    Find the force needed to accelerate a 20 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A body starts at 5 m/s and accelerates at 3.8 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the gravitational potential energy of a 20 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Solve using the quadratic formula: x² − 3x + 2 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A cylinder has radius 6 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A current of 7.9 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A population of 7,900 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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19. 19.

    A force of 14 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A device runs at 12 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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