Bangladesh · Class 12 · Practice Sheet 35

1. 1.

   Find the momentum of a 28 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A force of 103 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the gravitational potential energy of a 28 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A cone has base radius 2 cm and height 10 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.

   A current of 1.6 A flows through a 41 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 3 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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8. 8.

   A cone has base radius 2 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   Two masses 2,600 kg and 700 kg are 20 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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10. 10.

    A device runs at 208 V drawing 6.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Two masses 8,800 kg and 450 kg are 17 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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12. 12.

    A device runs at 217 V drawing 3.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object with initial velocity 9 m/s accelerates at 2.3 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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14. 14.

    Find the population standard deviation of: 9, 7, 8, 8, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A body starts at 14 m/s and accelerates at 1.4 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A population of 7,200 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    ৳ 700 is invested at 4% compound interest per annum for 3 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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18. 18.

    A wave has frequency 609 Hz and wavelength 1.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the momentum of a 10 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A device runs at 90 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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