Physics, asked by sitaramrampuriya, 11 months ago

The resultant of two vectors is perpendicular to one
of them and has the magnitude 4 m. If the sum of
the magnitude of two vectors is 8 m then their
respective magnitude are
(1) 4 m, 4 m
(2) 2 m, 6 m
(3) 3 m, 5 m
(4) 1 m, 7 m
- anar enoed of second's hand to hour​

Answers

Answered by Anonymous
28

Answer :-

3m and 5m

Option → C

Given :-

The resultant is perpendicular to one of the vector.

R = 4

Sum of magnitude of two vectors

= 8

To find :-

Their respective magnitude.

Solution:-

Let a and b be the magnitude of two vectors.

 a + b= 8m

Let ,Resultant is perpendicular to vector a.

 Tan\alpha = \dfrac{b sin\theta }{a + bCos \theta}

 Tan90^{\circ}=\dfrac{b sin\theta }{a + bCos \theta}

 \dfrac{1}{0} = \dfrac{b sin\theta }{a + bCos \theta}

  • Equating denominator with 0.

 a + b Cos \theta = 0

 b Cos \theta = -a

 Cos \theta = \dfrac{-a}{b}

Now,

Resultant is given by formula :-

 R = \sqrt{a^2 + b^2 +2ab Cos \theta}

  • Put the value of Cos \theta

 R = \sqrt{a^2 + b^2 + 2ab \times \dfrac{-a}{b}}

 R = \sqrt{a^2 + b^2 -2a^2}

 R^2 = b^2 - a^2

 (4m)^2 = b^2 -a^2

 16m^2 = (b+a)(b-a)

 16m^2 = 8m(b-a)

 b-a = \dfrac{16m^2}{8m}

 b-a = 2m

Now,

 a + b = 8m---1)

 b - a = 2 m----2)

  • Adding these two equation.

 a -a +b+b = 10m

 2b = 10m

 b = 5m

 a = 3 m

hence,

Magnitude of two vectors is 3m and 5m.

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