Nepal · Class 12 · Practice Sheet 27

1. 1.

   A 28 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A force of 57 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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3. 3.

   An object with initial velocity 7 m/s accelerates at 3.2 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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4. 4.

   Find the force needed to accelerate a 9 kg mass at 7.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A device runs at 46 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   In a triangle, a = 6, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   A body starts at 0 m/s and accelerates at 1.4 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Two masses 1,300 kg and 760 kg are 4 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 force of 62 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    An object with initial velocity 15 m/s accelerates at 4 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Rs 1,900 is invested at 3% compound interest per annum for 4 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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13. 13.

    Find the force needed to accelerate a 33 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    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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15. 15.

    A current of 4.2 A flows through a 38 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the population standard deviation of: 18, 17, 14, 3, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    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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18. 18.

    A force of 17 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A cone has base radius 12 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A triangle has sides a = 9 cm and b = 7 cm with an included angle C = 30°. 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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