Question

en
The maximum and minimum
magnitudes of resultant of two forces
are in ratio 5.3. Then find the ratio of
forces
10:6
None​

Answer 1

Answer:

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11th

Physics

Motion in a Plane

Mathematical Operations on Vectors

The ratio of maximum and mi...

PHYSICS

The ratio of maximum and minimum magnitudes of the resultant of two vectors

a

and

b

is 3:1. Now, ∣

a

∣ is equal to

November 22, 2019avatar

Hazel Dhir

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ANSWER

Resultant of two vectors is mark when angle b/w them is 0. Resultant is min when angle is 180.

∴

∣

∣

∣

∣

a

−

b

∣

∣

∣

∣

∣

∣

∣

∣

a

+

b

∣

∣

∣

∣

=

a

2

+b

2

−2ab

a

2

+b

2

+2ab

=

1

3

⇒a

2

+b

2

+2ab=9a

2

+9b

2

−18ab

⇒8a

2

+8b

2

−20ab=0

⇒2a

2

+2b

2

−5ab=0

Let a=x.b

⇒2x

2

b

2

+2b

2

−5ab

2

=0

⇒2x

2

+2−5x=0

⇒2x

2

−5x+2=0

⇒2x

2

−4x−x+2=0

⇒2x(x−2)−1(x−2)=0

⇒(2x−1)(x−2)=0

∴ x=2 or x=

2

1

⇒

a=2b

Explanation:

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