Nepal · Class 12 · Practice Sheet 8

1. 1.

   A wave has frequency 402 Hz and wavelength 1.48 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Two masses 8,900 kg and 650 kg are 5 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.

   In a triangle, a = 13, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   An object with initial velocity 14 m/s accelerates at 2.5 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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5. 5.

   A force of 310 N acts on an area of 2.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A wave has frequency 805 Hz and wavelength 3.03 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   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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8. 8.

   Find the gravitational potential energy of a 31 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 37 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A wave has frequency 513 Hz and wavelength 2.08 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the momentum of a 16 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A current of 4.7 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A device runs at 214 V drawing 9.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Solve using the quadratic formula: x² + 2x − 24 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A body starts at 8 m/s and accelerates at 4.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

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

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 12 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    An object with initial velocity 5 m/s accelerates at 4.5 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 force needed to accelerate a 47 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 6 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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