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From the formula F = (Gm1m2)/r2, if F = 100N, m1 = 5.0Kg and r = 2m, find G.

Physics

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Here are the solutions to the questions from the image:

1.

  1. Start with the given formula for gravitational force.

    F=GMmr2F = \frac{G M m}{r^2}
  2. To isolate GG, first multiply both sides of the equation by r2r^2.

    Fr2=GMmF r^2 = G M m
  3. Next, divide both sides by MmM m to make GG the subject of the formula.

    G=Fr2MmG = \frac{F r^2}{M m}

    The formula with GG as the subject is G=Fr2Mm\boxed{G = \frac{F r^2}{M m}}.

    2.

  4. Use the formula for GG derived in Question 1.

    G=Fr2MmG = \frac{F r^2}{M m}
  5. Substitute the given values into the formula

    F=100 NF = 100 \, \text{N}, M=5.0 kgM = 5.0 \, \text{kg}, m=3.0 kgm = 3.0 \, \text{kg}, and r=2 mr = 2 \, \text{m}.

    G=(100 N)(2 m)2(5.0 kg)(3.0 kg)G = \frac{(100 \, \text{N}) (2 \, \text{m})^2}{(5.0 \, \text{kg}) (3.0 \, \text{kg})}
  6. Calculate the square of rr and multiply the masses.

    G=100 N×4 m215 kg2G = \frac{100 \, \text{N} \times 4 \, \text{m}^2}{15 \, \text{kg}^2}
  7. Perform the multiplication in the numerator and then the division.

    G=400 N⋅m215 kg2G = \frac{400 \, \text{N} \cdot \text{m}^2}{15 \, \text{kg}^2} G≈26.67 N⋅m2/kg2G \approx 26.67 \, \text{N} \cdot \text{m}^2/\text{kg}^2

    The value of GG is 26.67 N⋅m2/kg2\boxed{26.67 \, \text{N} \cdot \text{m}^2/\text{kg}^2}.

    3.
    Gravitational potential is the work done per unit mass to move a test mass from infinity to a point in a gravitational field. It is always negative and is associated with mass.
    Electric potential is the work done per unit charge to move a test positive charge from infinity to a point in an electric field. It can be positive or negative and is associated with electric charge.

    4.
    Two processes of demagnetisation are:

    • Heating: When a magnetic material is heated above its Curie temperature, the increased thermal energy causes the magnetic domains to lose their alignment, resulting in demagnetisation.
    • Hammering/Mechanical Shock: Repeatedly striking a magnet or subjecting it to strong mechanical vibrations can disorient the magnetic domains, causing them to become randomly arranged and thus demagnetising the material.
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