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JIPMER 2012
Exam
JIPMER
Year
2012
Subject
Physics
Chapter
Mathematics in Physics

JIPMER 2012 · Physics · Mathematics in Physics

A certain vector in the x y -plane has an x -component of 4 m and a...

A certain vector in the xyx y-plane has an xx-component of 4 m and a yy-component of 10 m. It is then rotated in the xyx y-plane so that its xx-component is doubled. Then, its new yy-component is (approximately)

Options

  1. A20 m
  2. B7.2 m
  3. C5.0 m
  4. D4.5 m

Correct answer

B. 7.2 m

Step-by-step solution

Here, A=4i+10jA=4 \mathbf{i}+10 \mathbf{j} ∴∣A∣=(4)2+(10)2=16+100\therefore|A|=\sqrt{(4)^2+(10)^2}=\sqrt{16+100} =116 m=\sqrt{116} \mathrm{~m} Now, according to question, A=8i+njA=8 \mathbf{i}+n \mathbf{j} So, ∣A∣=(8)2+n2\quad|A|=\sqrt{(8)^2+n^2} ∴116=(8)2+n2\therefore \quad \sqrt{116}=\sqrt{(8)^2+n^2} Squaring on both sides 116=64+n2116=64+n^2 or n2=116−64=52n^2=116-64=52 or n=7.2 mn=7.2 \mathrm{~m}
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