Question

The resultant of two forces X and Y is Z. If Y is doubled, then new resultant will be perpendicular to X. Which option is correct?
(X=Y
X=Z
X+Y=Z
OV=Z​

Answer 1

Answer:

Hey,

Since we are given that X and Y  is Z

The magnitude of Z can be given by :-

=) Z² = X² + Q² + 2Cosθ …. (1)

where θ is the angle between X and Y  

Now, if Y is Doubled the new resultant S is perpendicular to X

=> cos 90 = ( X + 2Qcosθ ) / S

=> 0 = X + 2Qcosθ

=> cosθ =- X/2Q …… (2)

Putting Value of (2) in (1), we get

Z² = X² + Y² + 2XY(-X/2Y)

=> Z² = X² + Y² - X²

=> Z² = Y² Hence Z = Y or Z= X

Hence option b is correct

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peace!

Answer 2

So here we go,

We have,

vector X + vector Y = vector Z

using vector law of parallelogram,
The magnitude we get is,

${X}^{2} + {Y}^{2} + 2XY \cos( \alpha ) = {Z}^{2}$
----(i)



When vector Y is doubles we have it as vector(2Y),

Let the resultant be W, it's perpendicular to X,

i.e
vectorW = vector X + vector 2Y -----(ii)

Since the resultant is perpendicular to X,
Therefore,

(vector W)•(vector X) = 0,

And we have,


Let's mutiply both sides of (ii) with Vector X,

vector X•vector W = VectorX•vectorX + vector 2Y•vectorX


$0 = {X}^{2} + (2Y)(X) \cos( \alpha )$

----(iii)

Subtracting,
(iii) from (i),

${Y}^{2} = {Z}^{2} \\ \\ Y = Z$




Therefore the correct answer is Y = Z


which I'm assuming is the 4th option.