question_answer

     A particle of specific charge \[\frac{q}{m}=\pi \,\,Ck{{g}^{-1}}\]is projected from the origin towards positive x-axis with a velocity of \[10m{{s}^{-1}}\] in a uniform magnetic field \[\overset{\to }{\mathop{B}}\,=-2\hat{k}\,T\] . The velocity \[\overrightarrow{v}\]of particle after time = 1/12 s will be \[(in\,m{{s}^{-1}})\]

A) \[5[\hat{i}+\sqrt{3}\hat{j}]\]    

B)        \[5[\sqrt{3}\hat{i}+\hat{j}]\]

C) \[5[\sqrt{3\hat{i}}-\hat{j}]\]     

D)        \[5[\hat{i}-\hat{j}]\]

Correct Answer: B

Solution :

[b] Time period, \[T=\frac{2\pi m}{qB}=\frac{2\pi }{\pi \times 2}=1s\] Thus, particle will be at point P after  \[t=\frac{1}{12}s\] \[\overset{\to }{\mathop{v}}\,=10\left[ \cos \,30\hat{i}+\sin \,30\hat{j} \right]\] \[\overset{\to }{\mathop{v}}\,=10\left[ \frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j} \right]=5\left[ \sqrt{3}\hat{i}+\hat{j} \right]m{{s}^{-1}}\]