Nepal · Class 11 · Practice Sheet 25

1. 1.

   Two masses 5,900 kg and 730 kg are 6 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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2. 2.

   An object has mass 39 g and volume 13 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the momentum of a 60 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 10 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

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

   Formula:Quadratic Formula

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

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6. 6.

   A triangle has sides a = 10 cm and b = 17 cm with an included angle C = 45°. 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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7. 7.

   An object has mass 183.6 g and volume 27 cm³. Find its density.

   Formula:Density

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

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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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9. 9.

   A wave has frequency 641 Hz and wavelength 2.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A device runs at 40 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A current of 5.2 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A body starts at 5 m/s and accelerates at 5.2 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A cone has base radius 3 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A force of 33 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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16. 16.

    A body starts at 3 m/s and accelerates at 4.6 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Solve using the quadratic formula: x² + 5x + 0 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A wave has frequency 455 Hz and wavelength 1.74 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A device runs at 68 V drawing 0.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 7 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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