Tamil Nadu Board of Secondary EducationHSC Science Class 11

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is - Physics

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MCQ
Sum

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is

Options

  • 30°

  • 45°

  • 150°

  • 120°

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Solution

Given:

The resultant of `vecA` & `vecB` is perpendicular to `vecA` and the magnitude of the resultant (C) = `1/2 vecB` and α = 90°

Solution:

(i) Magnitude of resultant:

`C^2 = A^2 + B^2 + 2AB costheta`

`B^2/4 = A^2 + B^2 + 2AB(A/B)`

`-3/4B^2 = 3A^2 ⇒ B^2 = 4A^2` i.e. B = 2A

(ii) direction of resultant:

tan α = `(B sintheta)/(A + B costheta)`

∞ = `(Bsintheta)/(A + B costheta)`

A + B cos θ = 0

cos θ = `-"A"/"B" = -"A"/(2"A") = -1/2`

cos θ = `-1/2`

θ = `cos^-1(-1/2)`

θ = 120°

Concept: Elementary Concept of Vector Algebra
  Is there an error in this question or solution?
Chapter 2: Kinematics - Evaluation [Page 101]

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