A) \[{{n}_{1}}=4;{{n}_{2}}=1\]
B) \[{{n}_{1}}=8,{{n}_{2}}=2\]
C) \[{{n}_{1}}=6,{{n}_{2}}=2\]
D) \[{{n}_{1}}=4,{{n}_{2}}=2\]
Correct Answer: D
Solution :
Time period\[=\frac{\text{circumference}}{\text{velocity}}=\frac{2\pi r}{v}\] \[\therefore \]\[T\propto r/v\] Now, radius i.e., \[r\propto \frac{{{n}^{2}}}{Z}\]and velocity i.e., \[v\propto \frac{Z}{n}\] \[\therefore \]\[T\propto \frac{{{n}^{3}}}{{{z}^{2}}}\]for\[Z=1,T\propto {{n}^{3}}\] For given case\[{{T}_{1}}=8{{T}_{2}}\] \[\therefore \]\[{{n}_{1}}=2{{n}_{2}}\] So, option [d] satisfies the given condition.You need to login to perform this action.
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