India · Class 12 · Practice Sheet 41

1. 1.

   A 11 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Solve using the quadratic formula: x² + 1x + 0 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the momentum of a 53 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A body starts at 5 m/s and accelerates at 4.5 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A triangle has sides a = 9 cm and b = 6 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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6. 6.

   Solve using the quadratic formula: x² + 1x − 6 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A current of 6.4 A flows through a 50 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Two masses 3,500 kg and 850 kg are 2 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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9. 9.

   Find the momentum of a 60 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the gravitational potential energy of a 44 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A 14 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Two masses 8,200 kg and 850 kg are 9 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.

    A force of 109 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A body starts at 0 m/s and accelerates at 5.8 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    ₹3,300 is invested at 5% 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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16. 16.

    A body starts at 3 m/s and accelerates at 5.5 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 79 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A device runs at 17 V drawing 9.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A body starts at 12 m/s and accelerates at 3.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A wave has frequency 363 Hz and wavelength 0.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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