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If vectors A=cos wti + sin wtj and B= cos wt/2 i + sin wt/2 j are functions of time, then the value of t at which they are orthogonal to each other is
Options
(a) t = π/2w
(b) t = π/w
(c) t=0
(d) t = π/4w
Correct Answer:
t = π/w
Explanation:
Two vectors are,
A = cos ωt î + sin ωt ĵ
B = cos (ωt/2) î + sin (ωt/2) ĵ
For two vectors A and B to be orthogonal
A.B = 0
A.B = 0 = cos ωt.cos (ωt/2) + sin ωt.sin (ωt/2)
= cos [ωt – (ωt/2)] = cos (ωt/2)
So, ωt/2 = π/2
.·. t = π/ω.
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Topics: Motion in Plane
(93)
Subject: Physics
(2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
- A particle of mass 1mg has the same wavelength as an electron moving with a velocity
- A circular coil of radius 10cm and 100 turns carries a current 1 A.
- A solenoid 1.5 m long and 0.4 cm in diameter possesses 10 turns per cm length
- The particle executing simple harmonic motion has a kinetic energy K₀cos²ωt.
- If R is the radius of the earth and g is the acceleration due to gravity
Topics: Motion in Plane (93)
Subject: Physics (2479)
Important MCQs Based on Medical Entrance Examinations To Improve Your NEET Score
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