A) \[{{S}^{2/3}}\]
B) \[{{S}^{1/2}}\]
C) \[{{S}^{0}}\]
D) \[{{S}^{-5/3}}\]
Correct Answer: C
Solution :
[c] : As\[F\propto {{S}^{-1/3}},\] \[\therefore \]Acceleration,\[a\propto {{S}^{-1/3}}\] \[a=\frac{dv}{dt}=\frac{dv}{dS}.\frac{dS}{dt}=\frac{dv}{dS}v\]i.e.,\[v\frac{dv}{dS}\propto {{S}^{-1/3}}\] Integrating both sides, we get \[{{v}^{2}}\propto {{S}^{2/3}}\]or\[v\propto {{S}^{1/3}}\] As\[P=Fv\] \[\therefore \]\[P\propto {{S}^{-1/3}}{{S}^{1/3}}\]or\[P\propto {{S}^{0}}\]. i.e., power is independent of S.
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