A) \[\left[ 1\frac{1}{2},1 \right]\]
B) \[\left[ -\frac{1}{2},1 \right]\]
C) \[\omega \]
D) \[(1+\omega )(1+{{\omega }^{2}}(1+{{\omega }^{3}})(1+{{\omega }^{4}})\]
Correct Answer: D
Solution :
Total energy produced by the reactor in time t = 10 yr. \[r=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k}),\] \[r.(2\hat{i}+\hat{j}-3\hat{k})=-4\] \[r\times (-\hat{i}+\hat{j}+\hat{k})=0\]Efficiency\[r.(-\hat{i}+\hat{j}+\hat{k})=0\] Input energy caused by fission\[\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}\] \[3x+2y-2z+15=0,\] Energy produced by one fission of \[{{u}_{1}}\] \[{{u}_{2}}\] \[{{u}_{1}}\] Therefore, number of fissions required \[{{u}_{2}}\] \[{{u}_{2}}\] Hence, mass of uranium required is given by \[{{u}_{1}}\]\[{{u}_{1}}\]
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