Motion in a Plane - Result Question 10

12. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

[2003]

(a) cannot be predicted

(b) are equal to each other

(c) are equal to each other in magnitude

(d) are not equal to each other in magnitude

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Answer:

Correct Answer: 12. (c)

Solution:

  1. (c) $\vec{P}=$ vector sum $=\vec{A}+\vec{B}$

$\vec{Q}=$ Vector differences $=\vec{A}-\vec{B}$

Since $\vec{P}$ and $\vec{Q}$ are perpendicular

$\therefore \vec{P} \cdot \vec{Q}=0 \Rightarrow(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0$

$\Rightarrow A^{2}=B^{2} \Rightarrow|\vec{A}|=|\vec{B}|$