Philippines · Grade 11 · Practice Sheet 47

1. 1.

   Two masses 2,900 kg and 400 kg are 10 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.

   Find the force needed to accelerate a 24 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 108 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the gravitational potential energy of a 29 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A right-angled triangle has legs of 12 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

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

   Formula:Sum of a Geometric Series

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

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7. 7.

   A device runs at 177 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   An object has mass 32.5 g and volume 25 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A wave has frequency 478 Hz and wavelength 0.86 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A cylinder has radius 12 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Find the momentum of a 5 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A current of 2.3 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A 18 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A wave has frequency 364 Hz and wavelength 2.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    An object has mass 61.5 g and volume 41 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A population of 8,900 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A cylinder has radius 2 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A population of 4,300 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    ₱1,300 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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20. 20.

    A wave has frequency 739 Hz and wavelength 3.82 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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