Question

The sum of magnitude of two forces acting at a point is 18 and the magnitude of their resultant is 12. If the resultant is 90 degree with the force of smaller magnitude of forces.
a) 12,6
b)15,3
c)13,5
d)10,8
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Answer 1

Answer:

10, 2

Explanation:

let two forces a and b acting at a point p and c be their resultant in perpendicular to a

let a has smaller magnitude than be.

now refer the attachment.

HOPE THIS HELPS YOU...

Answer 2

AnswEr :

• The magnitude of the 2 vectors are 5 and 13. [ Option C ]

GivEn :

• Resultant force makes 90° angle with the smaller force.

• Sum of the two forces is 18 .

• Magnitude of their resultant is 12.

To find :

• Magnitude of the 2 vectors = ?

Solution :

Let the force of smaller magnitude be x and force of larger magnitude be y.

Now,

By Pythagoras theorem, [as the resultant angle is 90°with respect to hypotenuse (h) ]

As the resultant(R) force makes 90° with the smaller force x then y,

➝ R² = y² - x²

➝ 12² = y² - x²

➝ 144 = y² - x²⠀⠀⠀⠀⠀⠀−[eqn 1]

Sum of magnitudes of two forces is,

➝ x + y = 18

➝ y = 18 - x ⠀⠀⠀⠀⠀⠀−[eqn 2]

Substitute the value from eqn (2) in eqn (1), we get,

➝ y²- x² = 144

➝ (18 - x)² - x² = 144

➝ 324 - 36x + x² - x² = 144

➝ -36x = 144 - 324

➝ -36x = -180

➝ x = 180/36

➝ x = 5

Hence, smaller force is 5 .

Substitute the value of x in eqn (2),

➝ y = 18 - x

➝ y = 18 - 5

➝ y = 13

$\therefore$ Larger force is 13.

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