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

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

Nho · Answer

A. The expression of F in terms of d is  F =   2  0  0     / 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     Learn more about  variation :  https://brainly.com/question/14254277    #SPJ1

A. How to determine the expression

B. How to determine F when d = 10

C. How to determine d when F = 8 N

D. How to determine F when d is halved

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