A) \[14\,\,m\]
B) \[13.11\,\,m\]
C) \[10\text{ }m\]
D) \[2.0\text{ }m\]
Correct Answer: B
Solution :
Let A be vector in x-y plane. Its x and y components are \[{{A}_{x}}=12m\] and \[{{A}_{y}}=8m\] \[A=\sqrt{A_{x}^{2}+A_{y}^{2}}\] \[=\sqrt{{{(12)}^{2}}+{{(8)}^{2}}}\] \[A=\sqrt{208}m\] When the vector is rotated in x-y plane, then x component become halved and its new y component \[A_{y}^{'}=\sqrt{{{\left( \frac{{{A}_{x}}}{2} \right)}^{2}}+A_{y}^{'2}}\] \[\sqrt{208}=\sqrt{{{(6)}^{2}}+A_{y}^{'2}}\] \[A_{y}^{'}=\sqrt{208-36}\] \[A_{y}^{'}=\sqrt{172}\] \[=13.11\,\,cm\]
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