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:
- (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
$\therefore \vec{P} \cdot \vec{Q}=0 \Rightarrow(\vec{A}+\vec{B}) \cdot(\vec{A}-\vec{B})=0$
$\Rightarrow A^{2}=B^{2} \Rightarrow|\vec{A}|=|\vec{B}|$
