India · Class 12 · Practice Sheet 31

1. 1.

   A device runs at 127 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the gravitational potential energy of a 25 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   ₹2,400 is invested at 8% compound interest per annum for 2 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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4. 4.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   A wave has frequency 506 Hz and wavelength 2.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Two masses 8,300 kg and 780 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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7. 7.

   A population of 2,000 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A device runs at 151 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 23 kg mass at 8.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 34 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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12. 12.

    Two masses 6,300 kg and 740 kg are 16 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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13. 13.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Solve using the quadratic formula: x² − 9x + 18 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    Find the momentum of a 45 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Solve using the quadratic formula: x² − 2x − 8 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A force of 54 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the momentum of a 3 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 60 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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20. 20.

    A triangle has sides a = 20 cm and b = 9 cm with an included angle C = 90°. 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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