India · Class 9 · Practice Sheet 38

1. 1.

   Find the momentum of a 50 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A cone has base radius 6 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   Solve for x: 6x + 18 = 84.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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4. 4.

   A right-angled triangle has legs of 15 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   ₹72 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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6. 6.

   A device runs at 214 V drawing 6.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Solve for x: 6x + 17 = 65.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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8. 8.

   A force of 87 N acts on an area of 6.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Solve for x: 8x + 11 = 67.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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10. 10.

    Find the force needed to accelerate a 4 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the momentum of a 9 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A cylinder has radius 2 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    Solve for x: 7x + 12 = 33.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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14. 14.

    A wave has frequency 645 Hz and wavelength 1.05 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A force of 349 N acts on an area of 5.1 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the gravitational potential energy of a 25 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A 6 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A value changes from 54 to 255. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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20. 20.

    A train moves at 91 km/h for 5.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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