A) \[{{n}^{5/3}}:1\]
B) \[{{n}^{4/3}}:1\]
C) \[n:1\]
D) \[{{n}^{3}}:1\]
E) \[{{n}^{2/3}}:1\]
Correct Answer: A
Solution :
Volume of big drop\[=n\times \]volume of small drop \[\frac{4}{3}\pi {{R}^{3}}=n\times \frac{4}{3}\pi {{r}^{3}}\] \[R={{n}^{1/3}}r\] Capacitance of small drop, \[C=4\pi {{\varepsilon }_{0}}r\] Capacitance of big drop, \[C=4\pi {{\varepsilon }_{0}}R\] \[=4\pi {{\varepsilon }_{0}}{{n}^{1/3}}r\] \[C={{n}^{1/3}}C\] The potential of small drop\[V=\frac{q}{C}=\frac{q}{4\pi {{\varepsilon }_{0}}r}\] The potential of big drop \[V=\frac{nq}{(4\pi {{\varepsilon }_{0}}){{n}^{1/3}}r}\] \[V={{n}^{2/3}}V\] \[\therefore \]Energy of small drop\[=\frac{1}{2}C{{V}^{2}}\] Energy of big drop\[=\frac{1}{2}CV{{}^{2}}\] \[=\frac{1}{2}{{n}^{1/3}}C{{({{n}^{2/3}}V)}^{2}}\] \[={{n}^{5/3}}\frac{1}{2}C{{V}^{2}}\] \[\therefore \] \[\frac{Energ{{y}_{(big\,drop)}}}{Energ{{y}_{(small\,drop)}}}=\frac{{{n}^{5/3}}}{1}\]
You need to login to perform this action.
You will be redirected in
3 sec
