A. The expression of F in terms of d is F = 200 / d²
B. The force when the distance is 10 cm is 2 N
C. The distance when the force is 8 N is 5 cm
D. When the distance, d is halved, the force F becomes four times the initial force
<h3>A. How to determine the expression </h3>
From the question given above,
F ∝ 1 / d²
F = K / d²
Cross multiply
K = Fd²
But
F = 50 N
d = 2 cm
Thus
K = Fd²
K = 50 × 2²
K = 200 Ncm²
Therefore, the expression is given as
F = K / d²
F = 200 / d²
<h3>B. How to determine F when d = 10</h3>
- d = 10 cm
- K = 200 Ncm²
- F =?
F = K / d²
F = 200 / 10²
F = 2 N
<h3>C. How to determine d when F = 8 N</h3>
F = K / d²
8 = 200 / d²
Cross multiply
8 × d² = 200
Divide both sides by 8
d² = 200 /8
d² = 25
Take the square root of both sides
d = √25
d = 5 cm
<h3>D. How to determine F when d is halved</h3>
- Initial Force (F₁) = F
- Initial distance (d₁) = d
- Final distance (d₂) = 1/2 d = 0.5d
- Final final (F₂) =?
K = Fd² = constant
Thus
F₁d₁² = F₂d₂²
F × d² = F₂ × (0.5d)²
F × d² = F₂ × 0.25d²
Divide both sides by 0.25d²
F₂ = (F × d² ) / 0.25d²
F₂ = F / 0.25
F₂ = 4F
Thus, when the distance is halved, the force will increase by a factor of 4
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