A) \[\text{4}.\text{48 }\times \text{ 1}{{0}^{\text{6}}}\text{ m}/\text{sec}\]
B) \[\text{4}.\text{48 }\times \text{ 1}{{0}^{\text{7}}}\text{ m}/\text{sec}\]
C) \[\text{8}.\text{44 }\times \text{ 1}{{0}^{\text{6}}}\text{ m}/\text{sec}\]
D) \[\text{8}.\text{88 }\times \text{ 1}{{0}^{\text{7}}}\text{ m}/\text{sec}\]
Correct Answer: B
Solution :
\[eV=\frac{1}{2}m{{v}^{2}}\] \[\Rightarrow \] \[v=\sqrt{\frac{2eV}{m}}\] \[\Rightarrow \] \[\frac{v}{\sqrt{V}}=\sqrt{\frac{2e}{m}}=\]constant \[\therefore \] \[\frac{{{v}_{1}}}{\sqrt{{{V}_{1}}}}=\frac{{{v}_{2}}}{\sqrt{{{V}_{2}}}}\] \[\Rightarrow \] \[{{v}_{2}}={{v}_{1}}\sqrt{\frac{{{V}_{2}}}{{{V}_{1}}}}\] \[=3\times 2\times {{10}^{7}}\sqrt{\frac{5824}{2912}}\] \[\mathbf{=4}\mathbf{.48\times 1}{{\mathbf{0}}^{\mathbf{7}}}\mathbf{m/sec}\]
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