A) \[n=\frac{1}{2}\]
B) \[\operatorname{n} = 2\]
C) \[\operatorname{n} = \frac{1}{4}\]
D) \[\operatorname{n}=1\]
Correct Answer: B
Solution :
Work done \[\operatorname{W} = MB\left( cos {{\theta }_{1}} - cos {{\theta }_{2}} \right)\] In first case, \[{{\theta }_{1}}=0\,\,and\,\,{{\theta }_{2}}=90{}^\circ \] \[\Rightarrow \,\,\,\,\,\,\,\,{{\operatorname{W}}_{1}}=MB\left( cos\,\,0{}^\circ -\cos \,\,90{}^\circ \right)=MB\] In second case, \[{{\theta }_{1}} = 0{}^\circ and {{\theta }_{2}} = 60{}^\circ \] \[{{W}_{2}}=MB\left( 1-\frac{1}{2} \right)=\frac{MB}{2}\] Given, \[{{W}_{1}}=n{{W}_{2}}\] \[\therefore \,\,\,\,\,\,\,\,\,MB=n\frac{MB}{2}\,\,\,\Rightarrow \,\,n=2\]
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