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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    The x and y components of \[\overrightarrow{\text{A}}\] are 4 m and 6 m, respectively. The x and y components of \[(\overrightarrow{A}+\overrightarrow{B}\,)\]are 10 m and 9 m respectively. The magnitude of vector B is:

    A) 19 m    

    B)        \[\sqrt{27}\]

    C) \[\sqrt{45}\]      

    D)        \[\sqrt{50}\]

    Correct Answer: C

    Solution :

    [c] \[\text{\vec{A} = }4\hat{i}+6\hat{j}.\] If \[{{\text{B}}_{\text{x}}}\] and \[{{\text{B}}_{\text{y}}}\] are the components of vector along x and y axes, then             \[\text{4+}{{\text{B}}_{x}}\text{=10, }\therefore \text{ }{{\text{B}}_{x}}=6\] Also      \[\text{6+}{{\text{B}}_{y}}\text{=9, }\therefore \text{ }{{\text{B}}_{y}}=3.\] \[\text{Thus, B}\,\text{=}\sqrt{\text{B}_{x}^{2}\text{+B}_{y}^{2}}=\sqrt{{{6}^{2}}+{{3}^{2}}}=\sqrt{45}.\]


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