Question

Two forces are in the ratio of 7:5. The maximum and minimum of their resultants are in the ratio of (A) 5:2 (B) 2:5 (C) 6:1 (D)1:6
answer please
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Answer 1

✬ The maximum and minimum of their resultants are in the ratio of 6:1. Option c) ✬

Step-by-step explanation:

Given:-

• Two forces are in the ratio of 7:5.

To find:-

• The maximum and minimum resultant of the force

Required Formula:-

• F_max = F₁ + F₂
• F_min = F₁ - F₂

Solution:-

Where,

• F₁ = 7
• F₂ = 5

Applying the values,

$\\ :\implies\sf{F_{max}= F_1 + F_2}\\ \\ :\implies\sf{F_{max}= 7 + 5}\\ \\ :\implies\sf{F_{max}= 12}$

• The maximum resulant of the force is 12.

Finding the minimum resultant of the force,

$\\ :\implies\sf{F_{min}= F_1 - F_2}\\ \\ :\implies\sf{F_{min}= 7 - 5}\\ \\ :\implies\sf{F_{min}= 2}$

• The minimum resultant of the force is 2.

Now,Finding the force of maximum and minimum resultant.

$\\ :\implies\sf{\frac{F_{max}}{F_{min}} = \frac{ \cancel{12}}{ \cancel{2}}}\\ \\ : \implies \sf{ \frac{F_{max}}{F_{min}} = \frac{6}{1} }$

• Therefore,The maximum and minimum resultant of the force is 6:1.