Question

The force, F newtons, exerted by a magnet on a metal object is inversely "proportional to the square of the distance d cm."When d = 2 cm, F = 50 N
(a) Express F in terms of d.
(b) Find the force when the distance between the magnet and metal object is 10cm
(c) Find the distance between the magnet and metal object when the forc
(d) Explain what happens to F when d is halved.e is 8N.
Guys I need help with this especially the last one pls

Answer 1

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

A. How to determine the expression

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

B. How to determine F when d = 10

• d = 10 cm
• K = 200 Ncm²
• F =?

F = K / d²

F = 200 / 10²

F = 2 N

C. How to determine d when F = 8 N

• K = 200 Ncm²
• F = 8 N
• d = ?

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

D. How to determine F when d is halved

• 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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