Two forces A and B whose magnitude are in the ratio 3: 5 give a resultant of 28N . If the angle of their inclination is 60 ^ ° , then the magnitude of force B will be ----- N .

Correct answer: 20.00 Let A and B be the two forces. Then A = 3x; B = 5x, R = 28N and θ = 60 ^ ° . We know that R = A ^ 2 + B ^ 2 + 2ABcosθ ⇒ 28 = (3x) ^ 2 + (5x) ^ 2 + 2(3x)(5x)cos 60 ^ ° = 9 x ^ 2 + 25 x ^ 2 + 15 x ^ 2 = 7x ⇒ x = (28)/(7) = 4 Hence, force B = 5 × 4 = 20N

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Mathematics in Physics

NTA Abhyas 2020 · Physics · Mathematics in Physics

Two forces A and B whose magnitude are in the ratio 3: 5 give a...

Two forces

A

and

B

whose magnitude are in the ratio

3: 5

give a resultant of

28\text{N}

. If the angle of their inclination is

{60}^{°},

then the magnitude of force

B

will be -----

N

Correct answer

20.00

Step-by-step solution

Let

A

and

B

be the two forces.

Then

A = 3x; B = 5x, R = 28N

and

\theta = {60}^{°}

.

We know that

R = \sqrt{{A}^{2} + {B}^{2} + 2ABcos\theta}

⇒ 28 = \sqrt{{\left(3x\right)}^{2} + {\left(5x\right)}^{2} + 2\left(3x\right)\left(5x\right)cos{60}^{°}}

= \sqrt{9{x}^{2} + 25{x}^{2} + 15{x}^{2}} = 7x

⇒ x = \dfrac{28}{7} = 4

Hence, force

B = 5 \times 4 = 20\text{N}

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