Question

the greatest and least resultant of two forces acting at a point are 29N and 5N respectively ,if each forces is increased
by 3N find the resultant of two new forces acting at right angle to each other​

Answer 1

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Greatest when both are in same direction. Fmax = F1 + F2 =29 Kgf

Least when both are in opposite direction. F min=F1 -F2 =5 Kgf

So F1=17 and F2=12

Both increased So F1=20 , F2=15

Resultant force = ( 20*20 + 15*15)^1/2 = 25Kgf

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Answer 2

Answer:

The resultant of two new forces acting at right angle to each other is 25N.

Explanation:

Let the two forces be  A and B.

The greatest resultant of two forces= A+B = 29N------------------------1

The least resultant of two forces= A-B = 5N--------------------------------2

Solving the 1 and 2 equation

2A = 34N

A = 17N

Putting value of A in equation 1

17+B = 29

B = 29-17

B = 12N

Now, each force is increased by 3

--> A = 17+3 = 20N

    B = 12+3 = 15N

The forces are acting at right angle to each other --> theta = 90°

                                                                                        (Value of cos90° = 0)

Resultant = $= \sqrt{} A^{2} + B^{2} + 2AB cos theta\\= \sqrt{} (20)^{2} + (15)^{2} + 2*20*15*0\\= \sqrt{} 400 + 225$

                   = 25 N

Ans: The resultant of two new forces acting at right angle to each other is 25N.

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